creates research paper 2008-20 headlights on …...linkage, see e.g. bernstein et al (2000), almond...

CREATES Research Paper 2008-20

Headlights on tobacco road to low birthweight outcomes Evidence from a battery of quantile regression

estimators and a heterogeneous panel

Stefan Holst Bache, Christian M. Dahl and Johannes Tang Kristensen

School of Economics and Management University of Aarhus

Building 1322, DK-8000 Aarhus C Denmark

Working Paper

Headlights on tobacco road to low birthweight outcomes∗

Evidence from a battery of quantile regression estimators and aheterogeneous panel

Stefan Holst Bache · Christian Møller Dahl ·Johannes Tang Kristensen

Abstract Low birthweight outcomes are associated with considerable social andeconomic costs, and therefore the possible determinants of low birthweight are ofgreat interest. One such determinant which has received considerable attention is ma-ternal smoking. From an economic perspective this is in part due to the possibilitythat smoking habits can be influenced through policy conduct. It is widely believedthat maternal smoking reduces birthweight; however, the crucial difficulty in esti-mating such effects is the unobserved heterogeneity among mothers and the fact thatestimation of conditional mean effects seems potentially inappropriate. We provide aunified view on the estimation of relationships between prenatal smoking and birth-weight outcomes with quantile regression approaches for panel data and emphasizetheir differences. This paper contributes to the literature in three ways: i) we focus notonly on one technique, but provide evidence from several approaches and highlight avariety of statistical issues; ii) the performance of the methods are thoroughly testedin a simulated environment, and recommendations are given on their appropriate use;iii) our results are based on a detailed data set, which includes many relevant controlvariables for socio-economic, wealth and personal characteristics.

Keywords Quantile regression · low birthweight · panel data · unobservedheterogeneityJEL C13 · C23 · I10∗ This version: April 2011. First version: May 2008. This paper was previously titled “Determinants of

Birthweight Outcomes: Quantile Regression Based on Panel Data”

S. H. Bache, J. T. KristensenAarhus UniversitySchool of Economics and Management and CREATESTel.: +45-8924-1602E-mail: [email protected]: [email protected]

C. M. Dahl (corresponding author)University of Southern Denmark, OdenseDepartment of Economics and ManagementTel.: +45-6550-3267E-mail: [email protected]

2 Bache, Dahl, Kristensen

1 Introduction and Motivation

The potential adverse health consequences of low birthweight outcomes, along withthe considerable economic burden they are believed to impose on society, have at-tracted much attention by researchers in both medical and economic literature. Theuse of birthweight as a proxy for the general health condition of infants is common-place, as it has been linked to a vast array of health related complications, both short-and long-term.

The most severe event, perinatal mortality, has been found to be more likely in theevent of a low birthweight outcome. Several studies find statistical evidence of thislinkage, see e.g. Bernstein et al (2000), Almond et al (2005), and Black et al (2007).Furthermore, it is believed that low birthweight may lead to complications such asepilepsy, mental retardation, blindness, and deafness. For a review and references, seeHack et al (1995). While many of these complications are directly observable, somestudies also consider less obvious socio-economic implications of low birthweight, avery popular topic being school performance. Kirkegaard et al (2006) find a gradedrelationship between birthweight and school performance. In a follow-up study with5,319 Danish children aged 9–11, they conclude that the risk of reading, spelling andarithmetic disabilities is greater with low birthweight children. Similarly, Cormanand Chaikind (1998) find that repeating a grade, or special class attendance, is morelikely among low birthweight children. This may suggest that even future earningsand labour market outcomes may be affected by birthweight. According to Black et al(2007), this is indeed the case.

The strong evidence that low birthweight has adverse effects has naturally ledto substantial efforts towards identifying the determinants of these undesirable out-comes. One such determinant which has received much attention in the literature ismaternal smoking habits during pregnancy. Statistical efforts suggest a strong corre-lation between low birthweight and maternal smoking, see e.g. Bernstein et al (1978)and Permutt and Hebel (1989). Other studies examine the effect of smoking on someof the above-mentioned complications directly, e.g. Wisborg et al (2000), who findthat smoking increases the risk of the sudden infant death syndrome, Wisborg et al(2001), who find an increased risk of still birth and infant mortality from mater-nal smoking, and Linnet et al (2006), who link hyperactive-distractible behaviourin preschool children to intrauterine exposure to tobacco smoke. Medical researchgives several reasons why cigarette smoking may affect birthweight. An explanationthat seems to stand out is that the foetus may suffer from chronic hypoxic stress asa consequence of smoking. DiFranza et al (2004) and Hofhuisi et al (2003) explainthis phenomenon in part by a lowered maternal uterine blood flow and a reduction inoxygen diffusion across the placenta. An interesting observation is that smoking doesnot seem to have a significant adverse effect on all birth outcomes. Wang et al (2002)conclude that the association between maternal cigarette smoking and reduced birth-weight is modified by maternal genetic susceptibility, after having considered twospecific gene polymorphisms.

From an economic perspective, interest lies not with the individual as such, butrather with society as a whole. Maternal smoking habits are thus an especially inter-esting determinant since it is believed to be modifiable through policy conduct, e.g.

Headlights on tobacco road to low birthweight outcomes 3

by regulating taxes on tobacco products or by introducing smoking prohibitions inpublic areas. While medical research gives much attention to why smoking causeslow birthweight, the above has led economists to focus primarily on the extent ofthis effect, and the associated costs. This perspective has the advantage of allowinganalysts to disregard the specific medical links between maternal smoking and lowbirthweight, when using appropriate methods.

In an attempt to estimate the direct costs associated with low birthweight, Almondet al (2005) use data from hospitals in New York and New Jersey to find that thecosts peak at $150,000 (in year 2000 dollars) for newborns weighing 800 grams. Incontrast, an infant weighing 2,000 grams has an estimated associated cost of $15,000.The soaring costs at the low end of the birthweight distribution highlight an importantpoint. Using traditional mean regression will only uncover effects on the birthweightmean, i.e. infants weighing around 3,500 grams. One way to overcome this problemis to use a quantile regression approach, which can provide estimation results acrossthe entire distribution. This is done by Abrevaya (2001) and Koenker and Hallock(2001), who find justification for the quantile approach since regression estimatesvary throughout the distribution. It is, however, troublesome to consider the estimatedeffects as causal, because the analyses do not account for unobserved heterogeneity.Not only is the susceptibility of smoking effects among mothers different, as notedabove, but there are undoubtedly many other individual characteristics which cannotbe accounted for.

Econometric panel data models allow controlling for (time invariant) unobservedindividual heterogeneity. However, their extension to a quantile regression frame-work is still somewhat limited. In a recent paper, Abrevaya and Dahl (2008) con-sider the extension of the “correlated random effects” model by Chamberlain (1984)to a quantile regression framework, and estimate the effects of various birth inputson birthweight, using data from Arizona and Washington. Their results indicate thatthe negative effects of smoking, albeit present, are significantly lower in magnitudeacross all quantiles than the corresponding cross-sectional estimates.

This paper in part extends the results of Abrevaya and Dahl, using Danish data,which in itself is novel: no previous study has applied such techniques to data withthis origin. The advantage of our data, relative to those used in existing literature, liesin the richness and availability of variables. Quite naturally, however, there are fewerobservations due to a small geographical area. Finally, the Danish Civil RegistrationSystem allows perfect linkage of the data. Based on the idea of the above mentionedstudy, we consider a new correlated random effects specification for quantile regres-sion which, at the cost of a more restricted specification, allows for the use of anunbalanced dataset and benefits from a more parsimonious amount of regressors. Fi-nally, we consider fixed effects approaches to quantile regression, in particular weexamine a model specification by Koenker (2004) and suggest a simple a two-stagefixed effects approach.

Before we delve into our birthweight application in Section 3, we take a tour in therealm of quantile regression for panel data. Our treatment offers a unified frameworkin which the different approaches can be discussed and compared appropriately. Weare not aware of a similar discussion, and believe it to be novel and relevant more


generally. Simulations will serve to illustrate features and test performance of thediscussed estimation methods.

2 Econometric setup

2.1 Panel data and quantile regression - a prologue

A chief difficulty in examining the causal effect of prenatal smoking, and other rel-evant observable variables, on birthweight outcomes is the possible existence of in-fluential but unobservable determinants. The identification and measurement of allsuch determinants is an impossible task, and it can thus be necessary to control forsuch unobserved effects. When repeated measurements for each individual are avail-able, analysts will try to utilize this panel structure of the data to either filter out, orin some other way deal with e.g. time-invariant unobserved characteristics. There isa very well developed machinery with a variety of estimation procedures availablefor linear least-squares models, and hence the issues are here easily mitigated. Often,and indeed in the present analysis, the conditional mean of the response is not of pri-mary interest, but rather our attention is directed towards the conditional quantiles.Not surprisingly, combining the power of panel data methods with that of quantileregression methods is not a topic of little interest. While there are methods availableto do so, the topic is still relatively undeveloped, and there are some very importantsubtleties that often do not receive sufficient attention. In particular, one needs to bevery careful in defining the quantities or parameters of interest for reasons that wewill try to make clear. The main purpose of this section is to discuss some relevantprocedures for panel data quantile regression. Simulations will serve both to evaluatethe appropriateness of the methods and to investigate their performance. The discus-sion is of broader relevance than to the current analysis and we hope it will helpothers in choosing the best approach for their particular application.

There are many ways of introducing quantile regression. One can take a structuralapproach, assume a data-generating process (DGP), and describe how the error termmay change the coefficients at various quantiles. It is often hard to specifically linka DPG to its quantile function. Therefore, another common approach is to think ofan approximation to the quantile function directly, and not emphasize how data isgenerated. Angrist et al (2006) show that, in the linear case, the quantile regressionestimator in a certain sense gives the best linear approximation to the true conditionalquantile function. Related is the Skorohod representation where the response variableis generated by a (quantile) function that depends, amongst other things, on a rank-variable (or quantile index). We shall start the discussion with the following definitionof the conditional quantile function. Let Y denote the response variable, X be a vectorof covariates on which we condition, and τ ∈ (0,1) be the quantile index. We define

QY (τ |X)≡ inf{

y : FY (y |X)≥ τ}. (1)

Then, in Skorohod representation,

Y = QY (U |X), U |X ∼ uniform(0,1). (2)


It is well-known that the function is a solution to the minimization problem

QY (τ |X) ∈ argminqτ (X)

E[ρτ(Y −qτ(X))

], (3)

where ρτ(u) = (τ − 1{u < 0})u, and the minimization is over all measurable func-tions. It is also a solution to the estimating function E[Y ≤ qτ(X)] = τ , or equivalentlyE[τ−1{Y ≤ qτ(X)}] = 0. For an alternative to (3) for solving a parameterized versionof the latter estimating equation, see Bache (2010).

Our discussion is focussed on linear-in-parameters subsets of functions over which(3) is minimized, i.e. q(X ;β (τ)) = X Tβ (τ), and we shall investigate some possibleways of incorporating information from repeated measurements to alleviate identifi-cation issues that arise due to characteristics not included in the model. The methodswe discuss can be categorized into a fixed-effects and a correlated-random-effectsframework. The terminology is carried over from their least-squares analogies, andwe will not philosophize about the appropriateness of it. We will, however, now ar-gue why these two branches distinguish themselves even more from each other in aquantile regression setting.

Consider the following much simplified setup. We imagine a population of indi-viduals, where each can be either of two types, say c = 0 or c = 1. Types are attributesin the sense that they are constant and not under the individuals’ control (e.g. onecould think about genetic traits). The analyst has no information about types, i.e. forall purposes they are unobservable.

The question of interest is how a treatment x (e.g. smoking during pregnancy)affects the distribution of an outcome variable (e.g. birthweight). Figure 1 showsthree distributions that may be of interest.

Fig. 1: Three densities of Y : one conditional on c = 1 (dashed), one conditional on c = 0(dotted), and one unconditional of c (solid). All densities are here unconditional of x.

Now, if type is considered a part of the “noise” or “error term” in the model1,which it may well be, say to a politician who wants to start a campaign against pre-

1 In a treatment of quantile regression, “unexplained ranking mechanism” may be better terminology.


natal smoking, then the unconditional density is the relevant one. On the other hand,even though information in the data is not sufficient to reveal type, a doctor for exam-ple may have “inside” information on type, and would want a model that conditionson c. In this case, the conditional distributions are of interest. The main point here isthat the marginal effects of changes in X on the quantile function conditioning bothX and c are not the same as if conditioning only on X .

Fixed-effects approaches often incorporate estimates of c as a way of condition-ing on it, e.g. as the estimator by Koenker (2004). We will also suggest a simple2-stage plug-in method as a computationally simpler alternative. An inherent issuewith the fixed-effects methods is the incidental parameter problem that arises whenthe number of repeated measurements is small and fixed.

The correlated random effects model, suggested first for regression quantiles byAbrevaya and Dahl (2008), henceforth the AD model, tries to control for dependencebetween X and c, which can bias the estimates, if ignored, when a “random assign-ment” interpretation is wanted. The idea is that one can generate one or more “suf-ficient covariates” from the repeated observations which carry information that cancorrect for the bias. For the present application, we will also consider an alternativespecification that can be seen as a restricted version of the AD model, but which willallow us to use an unbalanced panel, and which is more parsimonious in terms ofnumber of regressors.

We formally define the four estimators in section 2.3, but first we present an illus-trative example of the point raised in this section about conditioning on unobservedtime-invariant variables.

2.2 An illustrative simulation experiment

Consider again the simple setup with a two-type population. The model that generatedthe data depicted in Figure 1 is generated as

ymb = xmb + cm +(1+ xmb + cm)εmb, b = 1,2; m = 1, . . . ,M, (4)

where one half of the population has cm = 1, the other cm = 0. The variable xmb isa binary treatment and equals 1 with probability 0.5+ 0.2cm. The disturbance εmbis a standard normal random variable. The subscripts m and b denote “mother” and“birth” respectively, and are chosen in the light of the birthweight application.2 Notethat the unobserved type affects both location and scale of the response distribution.We also define the counterfactual variables xmb and ymb, where xmb equals 1 withprobability 0.5 and ymb is determined by (4) with xmb in place of xmb. These thenrepresent a counterfactual world, where type has no impact on treatment probability.We will consider three “targets” for the estimate of a coefficient for the effect of being

2 In our application birth parity is what defines the waves, and does not represent time as such. In theexamples, however, one can think of b as representing time.


treated (setting x = 1):

∆τ : = QY (τ |xmb = 1)−QY (τ |xmb = 0) (5)

∆τ : = QY (τ | xmb = 1)−QY (τ | xmb = 0) (6)∆τ|c : = 1+Qε(τ) = 1+QN(τ), (7)

where QN(τ) is the τth quantile of a standard normal random variable.

Let β (τ) be the estimate from a quantile regression of ymb on xmb and β (τ) theone from a quantile regression of ymb on xmb and xm◦, where the latter variable isan average over the b dimension. Further, let β (τ) be the “oracle” estimate, whereknowledge of type is assumed, from a regression of ymb on xmb and cm. Table 1 showsthe results from a simulation experiment, comparing these estimators with the threetargets defined above for a single quantile index, τ = 1/5.

β (0.2) β (0.2) β (0.2)

∆τ

−0.0040 −0.0228 −0.0385(0.1188) (0.1619) (0.1295)

∆τ

0.0338 0.0070 −0.0087(0.1234) (0.1604) (0.1239)

∆τ|c0.0452 0.0184 0.0026

(0.1270) (0.1613) (0.1236)

(a) M = 999

β (0.2) β (0.2) β (0.2)

∆τ

0.0010 −0.0289 −0.0404(0.0380) (0.0597) (0.0567)

∆τ

0.0308 0.0009 −0.0106(0.0489) (0.0522) (0.0411)

∆τ|c0.0422 0.0123 0.0008

(0.0567) (0.0536) (0.0398)

(b) M = 9,999

Table 1: Bias and root mean squared error (in parentheses) for the three estimatorsβ (τ), β (τ), and β (τ) against the three targets ∆τ , ∆τ , and ∆τ|c. The simulation setupis τ = 1/5, “MC iterations”= 999, number of waves B= 2, and number of individualsM = 999 (panel a) and M = 9,999 (panel b). It should be noted that ∆τ|c can becalculated analytically, whereas ∆τ and ∆τ themselves are obtained by simulation.

The results in this example show quite clearly that the estimators estimate differ-ent quantities. A very noteworthy observation is that the estimator β (τ), a “correlatedrandom effects” type estimator that we will define below, does not try to estimate cm,and does not suffer from an incidental parameter problem. Instead, it uses informa-tion constructed from all observations for each individual to correct for correlationbetween cm and xmb to get a “random assignment” interpretation. The fixed effectsestimator, on the other hand, relies on some kind of estimate of cm (above it is sim-ply assumed known), and will most likely not perform as well as we have just seenwhen the number of waves is small. The last estimator is not really of interest, but itshows what happens with the usual quantile regression estimator when the treatmentis endogenous.


2.3 The estimators defined

Throughout, we take Ymb to be the random response variable and Xmb to be the cor-responding covariate vector. We denote by Zmb ⊂ Xmb a subset that has time-varyingand possibly endogenous covariates. The subscripts m and b (“mother” and “birth”)are chosen to reflect the dimensions in our birthweight study. Lower case letterswill denote outcomes in the sample with m = 1, . . . ,M and b = 1, . . . ,Bm. The pairs{Ymb,Xmb} are assumed to be independent and identically distributed (IID), and sowhenever no confusion arises subscripts m and b are omitted from notation.

For the purpose of this presentation of the models, we take the view that wecan approximate the conditional quantile function reasonably well by a linear-in-parameters specification, and will not argue a specific DGP.3 The following assump-tion states the standard QR problem in terms of the framework we shall work with todescribe the panel data approaches.

Assumption (A.QR): Linear quantile approximation representation. The class of func-tions over which (3) is minimized is linear, such that

qτ(X) = q(X ,τ) = X Tβ (τ) and (8)

Y = qτ(X ,U), (9)

where U is a rank variable with U |X ∼ uniform(0,1) (independently of X). For anytwo possible ranks u1 and u2 it is assumed that

u1 < u2⇔ q(X ,u1)< q(X ,u2)⇔ Y1 < Y2. (10)

Example: Normal location-scale model. Let

q(τ,X) = X Tβ (τ) = X T(β + γΦ

−1(τ)), (11)

where Φ is the standard-normal CDF, then we have the implied familiar location-scale DGP

Y = X Tβ +(X T

γ)Φ−1(U). (12)

The above representation in (8)–(9) is often referred to as the Skorohod representa-tion. If there are unobserved effects that affect both X and the ranking U , then wecannot represent the problem as above and use β (τ) as the quantity of interest, asillustrated in the example in the previous section. In the following, we will see howone can possibly get around this problem if such unobserved characteristics are time-invariant (or here, “birth-invariant”).

3 In our simulations, of course, we need to assume some data-generating mechanism.


2.3.1 Correlated random effects quantile regression

This presentation takes a slightly different approach than the one taken in Abrevayaand Dahl (2008), but the message remains the same. We now extend the model to in-clude unobserved characteristics Cm that partly determine Ymb either directly, throughZmb ⊂ Xmb, or both. These characteristics are assumed to be time-invariant character-istics, so dependence with Zmb is one-way. The random data pairs {Cm,Ym1,Xm1,Ym2,Xm2, . . .} are assumed to be IID. We wish to consider Cm a part of the unexplainedranking mechanism in the model, but at the same time control for endogenous effectspropagated through Zmb. To achieve this goal, we assume that repeated measurementsof Zmb allow for construction of sufficient covariate(s) Sm, and let the conditionalquantile function of interest be QYmb(τ |Xmb,Sm). Sufficiency is to be understood asto allow for the following extension of (A.QR). Again, we will often omit subscriptsto simplify notation.

Assumption (A.CRE): Correlated random effects representation. Consider a repre-sentation similar that of (A.QR), with

q(X ,S,τ) = X Tβ (τ)+ST

π(τ) and (13)Y = q(X ,S,U), (14)

for some variable S, constructable from repeated observations of Z, such that U |X ,S∼uniform(0,1).

This allows us to think of a response process Y (U) ≡ Y − STπ(U) as being Y “cor-rected” at level U for effects of C through Z, and as having τth conditional quantilesX Tβ (τ) for U = τ . Put this way, it is emphasized that the correction gives β (τ) theinterpretation of marginal effects in a “counterfactual world” where X is not deter-mined by C, but where C is allowed to work directly on Y through the ranking U .Figure 2 shows a simple graph of the assumed causal relations.

X\Z

CS - Z - Y

-

U

-

-

Fig. 2: The assumed relationship between variables in the model. The dashed lineindicates that Z |S,Y⊥U .

Under the assumptions in (A.CRE), the quantity of interest, β (τ), is identifiedfrom the data, and can be estimated by means of standard quantile regression of Y on


X and S, with empirical criterion function(π(τ), β (τ)

)= argmin

π,β

M

∑m=1

Bm

∑b=1

ρτ(ymb− sTmπ− xT

mbβ ). (15)

The separability assumption that the effects from C through Z can be captured byS in a linear fashion may not be as restrictive as one would think at first, since it isallowed to vary with τ . It may therefore provide a good linear approximation at eachquantile, and seems no more restrictive than believing the linear specification of q inthe first-place. In general, note that the assumptions do not restrict the effect from Cto a location-shift.

Example: Recall our previous introductory example. There we had a single endoge-nous binary treatment variable xmb (= zmb) and unobserved types cm that affect boththe probability of treatment, as well as location and scale of the outcome. Intu-itively, the mean of x (over b) carries information about type, and we let sm = xm◦ ≡∑b xmb/Bm. The simulations above confirmed that this was an acceptable choice andthat the procedure was appropriate in this case.

More specifically, we mention here the following two specific CRE models, in termsof constructing S; the one proposed by Abrevaya and Dahl (2008), and another whichcan be seen as a special case of the first.

The “AD” model: Assume (A.CRE), that the data constitutes a balanced panel Bm =B, and that Sm = (ZT

m1, . . . ,ZTmB)

T are sufficient covariates.

The “CREM” model: Assume (A.CRE), and that Sm = Zm◦, i.e. b-means of observedoutcomes of Zmb, are sufficient covariates.

The second, where the “M” in the acronym stands for mean, is the one deployed inthe previous example. It can be seen as a special case of the AD model, in whichS is essentially a weighed average, in the sense that the effect from C through Z isassumed to be the same for each b. In addition to being more parsimonious, in termsof number of regressors, this restriction allows the use of an unbalanced panel. It ispossible to extend the AD model, using dummy variables, to allow for some kinds ofunbalanced panels (Fitzenberger et al 2010).4

For the linear least-square analogues of the AD and CREM models, by Chamber-lain (1984) and Mundlak (1978) respectively, one has a linear DGP, ymb = xT

mbβ +cm + εmb, and one thinks of projecting cm onto observables as

cm = xTm1π1 + · · ·+ xT

mBπB,+ηm respectively (16)cm = xT

m◦π +ηm, (17)

for two models. For quantile regression, using a DGP as a starting point seems re-strictive as there is not necessarily a well-defined link between a DGP and a linearquantile representation. For further detail on—and a slightly different presentationof—the CRE approach we refer to the aforementioned article by Abrevaya and Dahl.

4 We thank the editor in chief for pointing this out to us. Our results did not seem to depend on thechoice of S, so we did not explore this option explicitly.


2.3.2 Fixed effects estimators

These estimators, in general, condition on the unobserved time-invariant characteris-tics C using some kind of estimate of them. Loosely speaking, the approaches in away model QY (τ |X ,C) by QY (τ |X ,C). As we saw in the previous simulation exam-ple, if one knows C, this approach is obviously perfectly valid, yet for a target quan-tity slightly different from that of the CRE approaches. Therefore, if one assumes thatgood estimates of C are available, these can be used in following representation.

Assumption (A.FE): Quantile regression conditional on fixed effects. The class offunctions over which (3) is minimized is linear in X and C such that

q(X ,C,τ) = X Tβ (τ)+Cδ (τ) and (18)

Y = q(X ,C,U), (19)

where U |X ,C∼ uniform(0,1) and satisfies an ordering property equivalent to that in(10) of (A.QR).

Essentially, the assumption here is that C is the only source of endogeneity and that itenters linearly on equal grounds with X . Conditioning on C will give β (τ) the sameinterpretation as if C was just another covariate and not a part of the unexplainedranking U .

However, in many cases the number of waves, Bm, is small (fixed) while M islarge. In such a setting, good estimates of M individual effects are hard to come by,a situation referred to as the “incidental parameter problem”. The estimates of C areusually not of particular interest, but it is not straight-forward to infer the conse-quences of M-inconsistent estimates of C on the estimates of β (τ).

Koenker (2004) suggested an interesting method to overcome some of the diffi-culties of the FE approach, in which estimation of C is intrinsic (i.e. it is a one-stepestimator). The idea is to (i) estimate the model for several τs simultaneously, re-stricting the effect of C at each τ to be the same; and (ii) penalize estimates of thefixed effects to shrink them towards zero. Both (i) and (ii) in some sense reduce thedimensionality added by introducing estimation of fixed effects. Again, our presenta-tion of the model is slightly alternative, compared to its original, such that it fits wellinto our framework.

“KFE(k): Koenker’s FE QR model”. Define M parameters, αm = Cmδ (τ) (for all τ).Assume that

q(Xmb,Cm,τ) = X Tmbβ (τ)+αm and (20)

Y = q(Xmb,Cm,Umb), (21)

Let τ1, . . . ,τk be k distinct quantile indices. Further define w1, . . . ,wk to be weightsthat define the relative impact of each of these indices on estimation. The parameters


in (20) are estimated from the following empirical criterion function:(β (τ1), . . . , β (τk), α1, . . . , αM

)=

argminβ1,...,βk,α1,...,αM

k

∑j=1

M

∑m=1

B

∑b=1

w jρτ j(ymb− xTmbβ j−αm)+λ

M

∑m=1|αm|. (22)

Let M→ ∞, B→ ∞ and Ma/B→ 0 for some a > 0. Then under some regularity con-ditions, β (τ j), j = 1, . . . ,k, are consistent and converge to Gaussian random vectors.See (Koenker 2004, Theorem 1) for the details.

It is pretty clear from this representation that the price one pays for the gained sparse-ness is that unobserved fixed effects are only allowed to affect Y by location shifts.Further, often B is fixed, and consistency is not guarantied by the theorem. The pa-rameter λ is a tuning/calibration parameter that allows one to control the impact of thepenalty, and how to choose it optimally is an open research question. When λ → 0,one has a (weighted) dummy variable regression, and when λ → ∞ the penalty setsall FE terms to zero, effectively leaving a pure (weighted) cross-section regression.As with other penalty methods, one might consider a “post-penalty” estimation ofthe model where terms shrunken to zero are omitted, since non-zero terms have beenaffected by the penalty. On the other hand, the penalty also helps “controlling” themany FE terms by not letting them take unreasonably large values.

A simpler approach, which does not restrict C to have the same impact acrossquantiles in return for sparseness, and which does not need calibration, is the fol-lowing two-step fixed effects estimator estimator, which resembles recent work byArulampalam et al (2007).

“2SFE: 2-step FE QR model.” Assume (A.FE). In a first step, obtain estimates Cm ofCm from a least-squares within groups estimation. In the second step, Cm are used inplace of C in (18), from which estimates of δ (τ) and β (τ) are obtained.

An important implicit assumption here is that a linear approximation is appropriatefor both the conditional expectation and the conditional quantiles. To hope for anyasymptotic justification, one would need B→ ∞, which we do not consider here, asit is not relevant for our application. It has come to our knowledge that Canay (2010)has work on the asymptotic aspect of this estimator. For our purpose, performance iscompared to Koenker’s method and the CRE estimators in the following simulationsection.

2.4 Additional simulation evidence

Indeed, the number of estimation methods under consideration allows for many in-teresting simulation setups. We have no desire of letting a simulation section eclipsethe main part of this section or the application in question. Therefore, we have chosena simple setup that highlights some important features and issues of the proceduresdiscussed. In short, our findings are:


• The CRE methods do not suffer from an incidental parameters problem and per-form well even when omitted effects have scale effects on the response.

• The CREM and AD models have very similar levels of performance.5

• FE methods generally have difficulty for short panels, and the size of the biasappears to depend critically on both τ and the actual setup. However:– estimating more quantiles simultaneously can be advantageous, and– post-estimating the “selected model” where penalized FE terms are removed

can improve performance in some cases.• The FE methods perform worse when cm has a scale effect (i.e. effects varying

over quantiles). For the KFE model, this is not surpising given its specification.• KFE estimates are generally bounded by cross-sectional estimates and a dummy-

variable quantile regression, as the theory suggests.• Being a FE estimator, 2SFE is also cursed by incidental parameters. It benefits

solely from simple estimation and from the fact that it needs no calibration.

Our simulation setup, which easily encompasses all of the estimation procedures,has the following data generating mechanism:

ymb = 10−3x1,mb + x2,mb + cm +ηmb (23)ηmb = (1+ x1,mb + γcm)εmb

εmb ∼ N(0,1)

where cm equals 0 with probability 1/2 and is distributed as standard normal other-wise; the binary variable x1,mb equals 1 with a probability, pm, that depends on cm inthe following way:

pm =

0.25 if cm > 0.20.75 if cm <−0.20.50 otherwise.

(24)

The idea is that the probability of treatment is only affected if individuals distinguishthemselves sufficiently. We let x2,mb be a sum of five uniform variables on (−0.5,0.5),which then lies in (−2.5,2.5). We can think of this setup as a simplified (and scaled)simulation of our birthweight application where we have an overall intercept, fromwhich some members of the population distance themselves (when cm 6= 0). Smoking,x1,mb, has a negative direct effect, and it has a scale effect. It is correlated with cmwhich makes it necessary to control for if we want to have some notion of randomassignment interpretation. The variable x2 plays the part of “other” observables inthe model. The parameter γ ∈ {0,1} lets us control whether cm has a scale effect inaddition to its location effect, which would cause the effect from cm to vary acrossquantiles.

As previously discussed, we have target quantities for the coefficient estimates onx1,mb that differ for CRE and FE approaches. Estimators in the latter category have thetarget β f e(τ) = QN(τ)−3, while those in the former have βcre(τ) = Qc+(2+γc)ε(τ)−Qc+(1+γc)ε(τ).

5 We have tried specifications where the dependence between x1,mb and cm depends on b to accommo-date AD. This, however, had little effect and CREM performed equally well.


τ = 1/4 τ = 1/2 τ = 3/4

FE -3.6745 -3 -2.3255CRE, γ = 0 -3.6299 -3 -2.3701CRE, γ = 1 -3.6114 -3.0253 -2.3797

Table 2: Coefficient targets for the estimators.

We report results for the following estimators: (i) A pure dummy variable quan-tile regression, (ii) KFE(1) and KFE(3); (iii) a post-penalty estimation of the latter,where penalized FE terms are removed; (iv) 2SFE; and (v) the two CRE methods.We also consider a cross-sectional estimate against both targets to evaluate the biaswhen ignoring cm completely. All results can be read in Tables 8 and 9 in AppendixA. Here, in the main text, we present a few selected results in Table 3. To illus-trate the asymmetric performance, particularly of the FE estimators, we considerτ ∈ {1/4,1/2,3/4}. The corresponding targets are presented in Table 2.

B = 2 B = 3 B = 5τ M = 499 M = 999 M = 499 M = 999 M = 499 M = 999

Cro

ss-s

ectio

nF

Eta

rget

0.25 −0.3380 −0.3402 −0.3412 −0.3443 −0.3435 −0.3405(0.3713) (0.3561) (0.3618) (0.3538) (0.3560) (0.3467)

0.50 −0.3724 −0.3740 −0.3755 −0.3718 −0.3718 −0.3722(0.3968) (0.3867) (0.3920) (0.3808) (0.3813) (0.3770)

0.75 −0.4321 −0.4344 −0.4310 −0.4282 −0.4186 −0.4245(0.4598) (0.4468) (0.4489) (0.4373) (0.4301) (0.4303)

Dum

my

regr

essi

on

0.25 0.6717 0.6626 0.3531 0.3474 0.1438 0.1431(0.6980) (0.6770) (0.3813) (0.3619) (0.1763) (0.1595)

0.50 −0.0028 −0.0119 −0.0047 −0.0055 −0.0035 −0.0053(0.1898) (0.1395) (0.1272) (0.0904) (0.0865) (0.0645)

0.75 −0.6773 −0.6864 −0.3596 −0.3598 −0.1438 −0.1475(0.7033) (0.7003) (0.3877) (0.3736) (0.1752) (0.1645)

KFE

3Po

stes

t.

0.25 0.0877 0.0807 0.1105 0.1081 0.0614 0.0600(0.1967) (0.1425) (0.1682) (0.1421) (0.1157) (0.0905)

0.50 −0.0224 −0.0321 −0.0474 −0.0430 −0.0253 −0.0269(0.1821) (0.1357) (0.1264) (0.0951) (0.0875) (0.0676)

0.75 −0.2531 −0.2582 −0.2052 −0.2002 −0.1040 −0.1086(0.3030) (0.2844) (0.2476) (0.2207) (0.1431) (0.1279)

2SFE

0.25 0.3921 0.3844 0.2598 0.2551 0.1563 0.1553(0.4285) (0.4014) (0.2882) (0.2707) (0.1844) (0.1687)

0.50 −0.0020 −0.0110 −0.0208 −0.0210 −0.0259 −0.0267(0.1640) (0.1169) (0.1162) (0.0844) (0.0879) (0.0664)

0.75 −0.4036 −0.4080 −0.3004 −0.2981 −0.1961 −0.2005(0.4355) (0.4249) (0.3262) (0.3101) (0.2155) (0.2104)

CR

EM

0.25 −0.0164 −0.0253 −0.0225 −0.0247 −0.0210 −0.0185(0.2063) (0.1416) (0.1439) (0.1029) (0.1020) (0.0739)

0.50 −0.0004 −0.0092 −0.0103 −0.0073 −0.0062 −0.0071(0.1749) (0.1237) (0.1290) (0.0916) (0.0904) (0.0638)

0.75 −0.0018 −0.0052 0.0048 0.0057 0.0144 0.0093(0.2017) (0.1398) (0.1431) (0.1030) (0.1045) (0.0745)

Table 3: Bias and root mean squared error (rmse) for simulation of (23) with γ = 0,i.e. no scale effect of the individual effects.

A few things should be mentioned here about the results. First, the choice ofpenalty parameter λ in practice is an unresolved problem. For this simulation we


have chosen one that approximately sets 30% of the FE terms to zero, i.e. “some butnot quite enough”. To get the same relative impact, this needs to be calibrated asB varies for a given N, but not vice versa. Second, the reported root mean squarederror results (rmse) cannot be compared across FE and CRE methods, since targetsand variance of the “total error” terms are different.

The cross section quantile regression suffers a serious bias away from both tar-gets. Note that it does converge to some quantity in the sense that, as the samplegrows, rmse and bias are more or less equal. The dummy variable regression per-forms very well for the median but not the other quartiles. Penalizing the FE termsand estimating all quantiles simultaneously offers improvements in the tails and post-estimating the “selected model” seems to add a little to this improvement. As ex-pected from the theory, as B grows these models perform better. The 2SFE modelperforms poorly, yet better than the dummy regression, both for γ = 0 and γ = 1. Ifone specifies Koenker’s FE method well, 2SFE is outperformed by it.

The CRE methods perform very well, and only the total sample size seems tomatter (i.e. no incidental parameters curse). They seem to be close to unbiased, withdiminishing variance. Table 9 in the Appendix shows that the FE methods cannothandle a scale effect of cm, and that they become even more biased. This is not thecase for the CRE methods, which still have high performance.

In conclusion, pooled cross-sectional estimation is rarely a good idea when thereare omitted individual effects correlated with included variables if a “random assign-ment” interpretation is intended. It also appears to be the case that one can do muchbetter than a pure dummy regression (at least in the tails). The FE methods suffer fromthe incidental parameters curse and high sensitivity to the data generating mechanism.It is possible to improve estimates in a FE setting by calibrating Koenker’s approach,but it is hard in practice to determine whether it is done optimally.

The CRE methods in general have good performance, and do not seem to havetrouble with either small B or scale effects of the individual effects. We need to stressagain that they estimate something different from the FE methods, and these findingsdo not imply that one should discard the latter. It all depends on what the target ofinterest is.

In any case, with a short panel it appears that the CRE results are more reliable.From an economic policy perspective the CRE target is perhaps also more sensiblein our birthweight application, as the politician is interested not in the individual assuch, but in society as a whole. Why then condition on individual effects? It is partof the unexplained ranking mechanism. In this light, we will put more emphasis onthe CRE results in our application. However, we will report a selection of FE resultsas well.

3 Data Description

We now return from our methodological excursion to put our birthweight applicationback in the spotlight. The data which are used throughout the analyses are in partobtained from Aarhus University Hospital, Skejby, in Denmark. In the Aarhus regionthis hospital is the only one with a maternity ward, and thus the data in fact represent


a broad population group, i.e. all economic and social classes. Furthermore, the dataare enriched with socio-economic characteristics of the mothers. These additionaldata have been made available by Statistics Denmark and are linked by means of theDanish Civil Registration System.

The methods we have discussed above require a panel of mothers with two ormore registered births. Only singleton births are included since multiple births babies(e.g. twins) tend to be lighter. Moreover, stillbirths are excluded, and thus the popu-lation of interest are singleton live births. For the variables of interest the data offeran unbalanced panel consisting of 16,602 births and 7,900 mothers. Except for theAD model, the estimation strategies discussed allow for an unbalanced panel, and thiswill be the primary data set. However, in the interest of comparison with this model,estimations have also been conducted on the basis of a balanced subset of the datawhich have been constructed with the first two births by each mother. This includes atotal of 12,670 births. The descriptive statistics for the (unbalanced) dataset are givenin Table 5. The sample ranges from the year 1992 to 2005. The included variablesand their role in the analysis are the topic of the remainder of this section.

The choice of birthweight as the dependent variable gives rise to an importantquestion: should gestational age be included as an explanatory variable? There isno doubt that gestational age is correlated with birthweight. However, in the presentanalysis our interest lies in the total effect of maternal smoking on birthweight, in-cluding any effects propagated through gestational age. Therefore it is not necessaryto include gestational age as an explanatory variable, it might even be inappropriate asit could have undesirable effects due to multicollinearity. In this context it should alsobe emphasised that on the matter of not including gestational age as an explanatoryvariable, we follow recent leading econometric studies on birthweight, see e.g. Abre-vaya (2006, 2001), Abrevaya and Dahl (2008), Chernozhukov (2010), and Koenkerand Hallock (2001).

The primary regressors of interest regard the mothers’ smoking habits. These arerepresented by two separate variables: whether or not mothers smoked at the timethey became pregnant (smoked before), and whether or not they smoked during thepregnancy (smoked during). Both variables are binary, as the data unfortunately donot offer details on smoked quantities. The analysis therefore cannot account for thesize of the treatment, which of course may be a drawback, since it seems reasonableto believe that quantity could be important. For identification of the separate effectsof the two smoke variables, it is necessary that there are mothers who actually start orstop smoking when becoming pregnant. 2,019 of 16,602 births are given by motherswho stop smoking at the time of pregnancy (12.66%). On the other hand only 10births are given by mothers who start smoking at the time of pregnancy (0.06%).Thus the change of behavior is therefore largely one-way.

The included variables can be roughly categorised into six categories. First, thereare variables relating to the behaviour of the mothers. Already mentioned are the twosmoke variables. Further, we include a variable, drink, which indicate whether or notthe mother has consumed alcohol during the pregnancy.6 Drinking habits are also

6 Here, alcohol is defined as consumption of more than 1 Danish standard drink (12 grams of purealcohol) per week.


believed to be harmful to the foetus and warnings are often explicitly printed on al-coholic containers. Related to the behavioural category is also the extent to which themother actively tried to become pregnant. Another possibility is that the pregnancywas either unwanted or accidental. To control for this, we include a dummy variablefor use of birth control pills within four months before becoming pregnant.

A second category that seems obviously related to the health of the baby, andthus possibly birthweight, is the general health or physical ability of the mother. Animportant variable in this category is occurrence of pregnancy complications, whichwe represent with an aggregated dummy variable which covers things such as prema-ture contractions, bleedings, excessive vomiting, infections, and intrauterine growthrestriction. Especially this last example is important, and may be caused by factorssuch as high blood pressure, heart disease, malnutrition, and substance abuse. A po-tential problem is that tobacco smoke may also be the source of this complication,and in effect leave us with an issue of separability of effects. This will be discussedfurther in the next section, where we present our results. The remaining variables inthis category are the number of doctor visits and prenatal visits during pregnancy,whether the mother has had diabetes at one or more of the registered pregnancies,and finally whether artificial insemination was required.

We also wish to control for effects related to wealth status, and thus include yearlyafter-tax income in 1,000 DKK, yearly unemployment benefits in 1,000 DKK and fi-nally home size measured in square meters. Here, the values are those registered forthe year of pregnancy. This category may be related to e.g. the ability to ensure goodsurroundings and a proper diet etc.

It has also previously been found that there is a linkage between birthweight out-comes and socio-economic factors such as marital status and level of education, seee.g. Abrevaya and Dahl (2008). We therefore include variables that indicate if themother was married during the pregnancy period, the mother’s education (a categor-ical variable summarised in Table 4, and included as dummy variables), and whetherthe mother was a student when pregnant. The latter variable may indicate how freelytime can be organised and may proxy for how stressful workdays are.

The final two categories concern characteristics of the mother and child respec-tively. They include height, weight, and age of the mother (the latter two are alsoincluded in squares), and dummy variables for birth parity and the sex of the child.

Category Description

0 No education.1 Primary school (9 years compulsory, 1 year optional).2 Secondary pre-university high school (3 years),

or technical college, craftsmen, etc.(2–5 years).3 College: short-cycle higher education programme (1–2 years).4 College: medium-cycle higher education programme (3–4 years).5 3-year academic (Bachelor) degree.6 5-year academic (Master) degree.7 PhD degree and above.

Table 4: Description of education categories.


A natural concern is whether or not there are relevant seasonality effects whichshould be controlled for. Buckles and Hungerman (2008) discuss whether the time ofyear affects birthweight and conclude that this is the case. They attribute such effectsto a strong correlation with socio-economic characteristics, which are well repre-sented in our data. Dehejia and Lleras-Muney (2004) investigate effects of unem-ployment rates on babies’ health, and suggest that high unemployment is positivelycorrelated with healthy babies. This is just one example of general year-specific phe-nomena which may have effects which are desirable to control for. In our analyseswe do this by including birth-year dummy variables.

The overall choice of variables is in part motivated by previous studies such asAbrevaya and Dahl (2008) and Koenker and Hallock (2001). Some results are there-fore comparable, and may confirm previous findings. To analyse the effect of mater-nal smoking, we use data on smoking both during and before pregnancy, allowing forsmoke to have a causal effect in different ways. This approach differs from previousstudies and relates to the discussion of whether “last-minute” intervention could beeffective.

1st child 2nd child 3rd child 4th child

Variable Mean Std.dev. Mean Std.dev. Mean Std.dev. Mean Std.dev.

Birthweight 3503.82 (534.17) 3650.23 (531.20) 3674.22 (554.12) 3624.56 (547.75)Smoked during 0.14 0.13 0.16 0.21Smoked before 0.30 0.24 0.25 0.28Drink 0.04 0.03 0.04 0.03Birth control pills 0.26 0.16 0.14 0.11Complications 0.22 0.25 0.28 0.26Doctor visits 3.07 3.00 2.94 2.80Prenatal visits 5.17 4.74 4.56 4.47Test tube baby 0.02 0.01 0.00 0.01Diabetes 0.01 0.01 0.02 0.03Income 107.04 (40.65) 135.62 (105.72) 149.39 (67.37) 151.94 (50.48)Unemployment benefits 6.43 (17.41) 6.97 (18.57) 6.29 (17.98) 4.37 (14.52)Home size 93.64 (45.20) 112.74 (44.26) 125.59 (43.71) 131.47 (44.26)Married 0.43 0.65 0.76 0.72Student 0.23 0.14 0.09 0.08Education cat. 0 0.01 0.01 0.01 0.01Education cat. 1 0.13 0.12 0.17 0.29Education cat. 2 0.49 0.42 0.37 0.32Education cat. 3 0.05 0.06 0.04 0.03Education cat. 4 0.18 0.23 0.25 0.21Education cat. 5 0.05 0.04 0.03 0.02Education cat. 6 0.09 0.12 0.12 0.10Education cat. 7 0.00 0.01 0.01 0.01Height 168.56 (6.04) 168.57 (6.07) 168.20 (6.03) 167.36 (5.95)Weight 63.92 (10.83) 65.24 (11.89) 65.79 (12.37) 65.71 (12.40)Age 27.57 (3.75) 30.34 (3.82) 32.47 (3.83) 33.99 (4.18)Male child 0.51 0.50 0.51 0.52

Birthweight quantiles

Quantile 1st child 2nd child 3rd child 4th child

10% 2880 3030 3030 300225% 3200 3330 3350 330050% 3500 3650 3660 365075% 3850 4000 4020 399090% 4150 4300 4350 4288Observations 6642 7416 2181 363

Table 5: Descriptive statistics for the Aarhus Birth Cohort.


4 Results

We consider our main estimation results to be the CRE estimates; especially those forthe unbalanced panel and the CREM specification. From an economic policy perspec-tive, the interpretation of the CRE estimates seems most appropriate: to the politicianunobserved individual effects should be part of the unexplained ranking or distribu-tion mechanism, yet for estimation purposes some notion of random assignment iscalled for to take into account the dependence between the unobserved and includedcovariates. Also, the CRE estimators are not cursed by incidental parameters. Theirspecifications give no reason why they should be, and indeed our simulations con-firmed their good performance, also for short panels.

The FE estimators, on the other hand, are questionable in such a setting. We givesome insight into some bounds for some available calibration options and argue that,even though the estimators are cursed, they seem to lead to conclusions that are diffi-cult to refute.

Investigating the alleged negative effects of smoking behavior on birthweight out-comes is a prime objective in this analysis. Therefore we initiate the presentation ofour results with a detailed discussion of the matter, using evidence from our batteryof estimators, after which we elaborate on some of our other findings.

Table 6 summarizes the results for the smoked during variable as estimated by avariety of methods. These surely have one thing in common: a statement that prenatalsmoking do not have negative direct effects on birthweight would be hard to justify,given the evidence from any of the estimators.

Consider first the results for the unbalanced data set.7 Overall, the cross-sectionestimates provide the largest estimates (in absolute value) of the smoking effect. Thisholds, not only for the methods and calibrations shown here, but for all the manyvariations we have tried. The CREM “correction” estimates, S(CREM), absorbs an in-creasing part of the large effect alleged by a pure cross-section estimator, the furtherwe move to the right in the birthweight distribution. This indicates that in the left tail,where we then have the largest adverse effect smoke during pregnancy, dependencebetween smoke and unobserved individual effects does not interfere much. Suppos-edly, there is more such “joint dependence” with birthweight at the larger quantiles.This supports a conclusion that smoking is more severe where it hurts the most: wherebabies are already prone to be low achievers when it comes to birthweight. In fact,all estimators except for 2SFE, lead to the conclusion that the adverse effect relativeto birthweight is increasing to the left in the distribution when comparing point esti-mates to birthweight quantiles reported in Table 5. The 2SFE estimator here predictsa constant relative effect.

The KFE estimator can generally be calibrated to give results that lie betweenthose of a pure dummy-variable estimator and a pure cross-section estimator. We willshortly discuss this in a little more detail. In our application, a pure dummy-variableregression is numerically infeasible. Letting λ → 0 to approach the dummy-variableestimates, we learn that the effect of smoking decreases in absolute value. No value

7 For all our estimations we have used a blocked pairwise subsampling bootstrap, as deemed appropriateby Abrevaya and Dahl (2008). The idea is that when sampling a mother, all her births are included to dealwith the dependence in the observations.


Estimates for smoked during Quantile Regressions

10% 25% 50% 75% 90%

Unb

alan

ced

data

CS -188.063 *** -181.629 *** -169.165 *** -177.479 *** -200.441 ***

(28.681) (22.116) (18.526) (21.528) (27.491)

CREM -190.485 *** -112.107 *** -75.991 *** -90.337 *** -2.081(49.047) (35.800) (27.952) (34.573) (49.101)

S(CREM) 1.511 -81.205 * -118.446 *** -118.538 *** -224.515 ***

(60.811) (47.264) (36.936) (44.050) (57.950)

KFE(5), λ = 0.8 -161.989 *** -163.087 *** -155.812 *** -148.444 *** -167.575 ***

(26.249) (18.478) (16.592) (19.996) (24.541)

KFE(5), λ = 0.8, post-est. -162.821 *** -156.776 *** -146.783 *** -186.265 *** -183.513 ***

(32.061) (24.873) (24.113) (25.319) (32.148)

2SFE -70.869 *** -83.486 *** -99.452 *** -104.189 *** -108.669 ***

(26.305) (21.007) (19.840) (20.379) (24.320)

Bal

ance

dda

ta

CREM -247.002 *** -154.444 *** -88.071 *** -110.895 *** 3.708(54.908) (39.487) (32.845) (41.679) (59.003)

S(CREM) 76.550 -24.508 -98.878 ** -81.969 -214.324 ***

(67.040) (48.564) (39.680) (50.903) (69.351)

AD -231.362 *** -174.003 *** -57.873 -126.478 *** 12.694(58.602) (39.997) (35.973) (44.777) (61.797)

S1(AD) 34.427 17.522 -52.118 * 19.774 -32.024(48.437) (33.175) (30.156) (36.824) (51.533)

S2(AD) 37.590 -21.545 -77.352 ** -88.525 ** -184.486 ***

(48.435) (37.411) (34.246) (41.459) (54.086)

Asterisks denote the significance level (double-sided). *: 10%, **: 5%, ***: 1%.Bootstrapped standard errors are given in parentheses. The bootstrap was done using a sample size of 3,000births and 499 iterations.

Table 6: Results for smoked during from a selection of estimators. The S(·)-results arefor the added CRE variables constructed from repeated measurements of smoke during (seethe last part of Section 2.3.1). For the KFE estimates, λ refers to the penalty parameter, and“post. est” is where the model is re-estimated without penalty and zero-FE-terms.

of λ , however, leads to effects of smoking as small as claimed by the 2SFE estimator.The value of λ is non-negligible, and we are not aware of a practical rule for choosingit appropriately. However, our simulations confirm that the performance of the KFEestimator can be calibrated to outperform the 2SFE estimator. Since the latter acts likea lower bound in our case, there is strong evidence that there are significant directadverse effects from smoke during pregnancy, also from a fixed effects perspective.However, there is much uncertainty about how adverse. The choice λ = 0.8, for whichthe results are reported in the table, penalizes to a degree where 30% of the mothersshare intercept, and the remaining 70% are sufficiently different to get their own.Re-estimating the selected model has a more pronounced effect in the right tail. Anargument for re-estimation is that the penalty affects the non-zero FE terms, whereasan argument against re-estimation is to preserve some degree of control over the sizeof estimated individual effects.

In the lower part of Table 6, we provide CRE results from the smaller balancedpanel. We include this mainly to show that the AD and CREM specifications give verysimilar estimates, justifying the more simple CREM specification of S which thenallows for the inclusion of more observations given by the unbalanced panel. The


point estimates for the balanced panel indicate a slightly larger effect, compared tothe unbalanced one, even though we cannot deem them statistically different. Oneexplanation, however, could be that mothers who give birth to unhealthy babies (interms of low birthweight) choose not to get a third or fourth child, this resulting insome kind of sample selection issue. This would again point to the unbalanced panelas the more appropriate.

A general point that we need to emphasize is that even at the first decile birthsare not categorised as low birthweight (often defined as 2,500 grams), cf. Table 5.Unfortunately, it is not possible to obtain reasonable results for lower quantiles dueto the very few extreme observations. However, it does not seem reasonable to expectthe adverse effects of smoking to diminish as we move into the extreme left of thedistribution. In fact, the trend in the CRE models suggests exactly the opposite. Toillustrate the trend visually we have plotted point CRE estimates for a whole range ofquantiles in Figure 3 (left panel). For comparison we show some FE estimates in theright panel. As KFE(k) estimations are problematic for such a “grid”, we use a KFE(1)specification. The right panel, where we also include the cross-section estimates, alsoserves to illustrate how estimates move as a function of λ .

0.2 0.4 0.6 0.8

-200

-150

-100

-50

Quantile, τ

AD

CREM balancedCREM unbalanced

Quantile, τ

0.2 0.4 0.6 0.8

2SFE

KFE(1), λ = 0.5KFE(1), λ = 1.0KFE(1), λ = 1.5Cross-section

Fig. 3: Smoke during estimates plotted for a grid of quantile indices and estimators.The gray areas show the bootstrapped 90% and 95% confidence intervals.

To add a little insight into what happens when varying λ , we consider the KFE(5)point estimates for smoked during and the ratio of FE terms shrunken to zero as afunction of λ . We present this sensitivity analysis in Figure 4. The top panel shows


how the effect decreases at all quantiles as we penalize more. The trend stops atλ ≈ 1.6 where the bottom panel shows that almost all FE terms are set to zero. Wealso show the penalized ratio for KFE(1). It seems that FE terms are (fully) affectedby the penalty in chunks. This feature is most pronounced for KFE(1), and it appearsthat this effect is smoothed out for KFE(k) as k increases.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-200

-160

-120

-80

Smok

eddu

ring

τ = 0.10τ = 0.25τ = 0.50τ = 0.75τ = 0.90

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.2

0.4

0.6

0.8

1.0

Penalty, λ

Rat

ioof

fixed

effe

cts

sett

o0.

τ = 0.10τ = 0.25τ = 0.50τ = 0.75τ = 0.90KFE(5)

Fig. 4: The top panel shows the KFE(5) estimates for smoked during as the penaltyparameter λ varies. The bottom panel shows the ratio of FE-terms shrunken to zerobecause of the penalty as a function of λ .


Our analysis, of course, also includes data on whether the mothers smoked be-fore their pregnancies. Interestingly, however, this seems to be unimportant when itcomes to birthweight: no estimators find noteworthy significance. We therefore donot present a similar discussion for this variable, although some results can be foundin Appendix B. We find the absence of statistical significance a very important andquite comforting result. It suggests that smoking behavior prior to pregnancy is notcrucial for birthweight outcome, and it gives future mothers who are smoking a verygood argument to quit in time. Intervention policy can therefore prove profitable, asreducing the number of low birthweight babies reduces both monetary as well associo-economic costs.

Maternal smoking is also one of the prime interests in the study by Abrevaya andDahl (2008), which is based on American data, more specifically natality data fromWashington and Arizona. In their study they only have a smoke variable comparableto our smoked during, but for this variable they also find significant negative effects.However, their findings suggest somewhat less severe effects, in the range around−80 to −60 grams. Whether this can in fact be attributed to actual differences oris a consequence of measurement error is hard to say, but the latter could perhapsbe attributed to smoking being less of a taboo in Denmark, which could lead to alower degree of misreporting. Furthermore, they find that cross sectional estimatesexaggerate the effect of smoking even more than in this case.

In addition to the variables pertaining to maternal smoking our analysis also con-tains a number of other interesting variables. A set of results for the CREM modelusing the unbalanced dataset is given in Table 7. Again, we will focus on these resultsand only consider those from the other models on a few occasions. A complete setof results for all the models is available as a separate appendix, and the most relevantresults are listed in Appendix B. For the CRE-specifications we use all variables thatvary from birth to birth to construct Sm, except education and year dummy-variables.The variables height and diabetes do not vary in our sample and are therefore notused, either for Sm or in the fixed effects model.

One behavioural aspect which receives great attention, especially related to preg-nancies, and which is the subject of much societal debate, is drinking habits. This isalso a topic where policy is conducted in the attempt to affect people’s behaviour, e.g.taxes and age restrictions on the purchase of alcohol. In the light of the strong beliefthat alcohol intake during pregnancy has negative health implications on the foetus,it seems puzzling that these estimations show no significance in the CREM model andno or very little in the other models considered. There could be many reasons why nosignificance shows up in our results, one of which could be measurement or reportingerrors. Even so, drinking may be the cause of many other health implications whichare not related to birthweight.

In the behaviour category we also have the variable birth control pills. As men-tioned earlier this can be thought to proxy for whether the pregnancy was plannedor not. We do see some signs of significance for this variable, but the extent of thisvaries between models. However, in general the point estimates are negative as wouldbe expected if it indeed acts as a proxy for unwanted pregnancies.

In the health category of variables we have three variables which show clearly sig-nificant effects. Prenatal visits are of special interest since it is a preventive measure


Quantile Regressions

10% 25% 50% 75% 90% OLS

Smoked during -190.485 *** -112.107 *** -75.991 *** -90.337 *** -2.081 -94.897 ***

(49.047) (35.800) (27.952) (34.573) (49.101) (23.618)

Birth control pills -27.853 -52.478 *** -28.928 ** -21.657 -19.116 -33.813 ***

(25.097) (18.130) (14.118) (16.678) (22.708) (11.650)

Complications -122.386 *** -67.361 *** -46.073 *** -29.562 ** -11.029 -65.723 ***

(24.632) (16.595) (12.271) (14.727) (21.520) (10.636)

Prenatal visits 109.582 *** 90.162 *** 77.477 *** 80.245 *** 73.484 *** 64.011 ***

(11.583) (5.906) (4.583) (5.080) (6.969) (11.670)

Test tube baby -2.683 64.214 30.674 -57.277 -251.771 *** -34.417(108.153) (70.387) (61.737) (63.434) (86.622) (46.240)

Diabetes 181.554 * 217.704 *** 280.896 *** 315.398 *** 373.631 *** 282.529 ***

(94.004) (70.214) (55.456) (62.333) (88.341) (54.962)

Student 20.743 4.311 1.137 10.260 51.933 * 17.787(31.961) (22.674) (21.060) (22.319) (29.430) (15.434)

Height 6.662 *** 8.423 *** 10.489 *** 11.419 *** 11.183 *** 10.269 ***

(1.525) (1.088) (0.975) (1.074) (1.320) (0.906)

Weight 5.722 2.412 -8.622 2.040 23.161 ** 7.950(14.546) (9.823) (8.403) (8.182) (11.050) (6.514)

Weight2 -0.026 0.008 0.063 -0.010 -0.127 * -0.036(0.099) (0.066) (0.058) (0.054) (0.071) (0.043)

Age -40.769 -24.258 -19.409 -29.653 * -0.204 -14.971(30.152) (20.280) (16.161) (17.768) (26.393) (14.840)

Age2 0.867 * 0.516 0.402 0.465 0.065 0.333(0.467) (0.319) (0.256) (0.285) (0.420) (0.236)

Second child 177.725 *** 162.143 *** 150.112 *** 175.701 *** 156.739 *** 162.162 ***

(21.562) (14.632) (12.540) (14.267) (19.457) (11.515)

Third child 213.334 *** 191.121 *** 190.076 *** 252.706 *** 231.066 *** 209.153 ***

(33.522) (24.012) (22.312) (24.301) (31.575) (20.485)

Fourth child 172.238 *** 182.380 *** 181.915 *** 233.246 *** 202.214 *** 191.631 ***

(56.800) (41.156) (37.683) (40.316) (51.240) (34.217)

Male child 121.921 *** 128.415 *** 137.299 *** 162.926 *** 186.615 *** 145.904 ***

(16.220) (12.039) (10.115) (12.611) (16.705) (8.042)

Asterisks denote the significance level (double-sided). *: 10%, **: 5%, ***: 1%.Bootstrapped standard errors are given in parentheses. The bootstrap was done using a sample size of 3,000births and 499 iterations.

Table 7: Results for the CREM estimation using the unbalanced data set. Insignif-icant variables are not reported here but in Appendix B. These are: smoked before,drink, doctor visits, income, unemployment benefits, home size, married, and all edu-cation categories. Dummy variables for birth year are mostly significant but removedfrom this table in the interest of space. Results for the constructed CRE variables (i.e.those in Sm) can also be found in Appendix B. The OLS estimates are from a Mundlakregression with the projection being the same as Sm.

intended to ensure good health of the foetus, and therefore its effect is of great interestto policy makers. The main problem with prenatal visits, however, is that there maybe two reasons for consulting a midwife, either as a routine/precautionary measure orbecause of complications. It is not possible to directly distinguish between these twoeffects of the variable. Therefore the estimations also include complications, whichin part controls for this, thus leaving us with the preventive effect. We see that pre-natal visits are significant, indicating a positive preventive effect. Further, complica-tions have a significant negative effect as would be expected. However, this variableis problematic, as indicated in the last section, since it includes cases of intrauter-


ine growth restrictions, which may be one of the channels through which smokingreduces birthweight. It is not possible to separate out this part of the variable, andconsequently as a robustness check regressions have been run without complications.The resulting outcome had only minor changes in the point estimates and did notalter any conclusions. On this basis it is concluded that the prevalence of intrauterinegrowth restrictions does not constitute a problem for the interpretation of the results,in particular those for smoked during.

The last significant variable in this category is diabetes, which has a positiveeffect on the right tail of the birthweight distribution. This is in accordance with themedical literature, where diabetes is commonly accepted as a birthweight-increasingfactor. Finally, both doctor visits and test tube baby show only little significance inthe CREM model. In a few cases, they show moderate significance in the fixed effectsmodels. The former can be thought of as a general measure of the mother’s health.However, it is hard to say how good a proxy it really is, since it represents, not onlybirth-related health, but also general illness or even hypochondria. The fact that thelatter is mostly insignificant need not say anything about causality, but may be due toa very small number of test tube babies in the sample.

The variables in the wealth and socio-economic categories are in general all in-significant. We do, however, see two exceptions. First, the variable student is mostlysignificant in the fixed effects models, which is in contrast to the CRE models. Sec-ond, the education variables do show moderate signs of significance in some of thefixed effects specifications, but there is not any general consensus on the significancebetween the models. That these categories are largely unimportant is not particularlyunexpected when considering the welfare system in Denmark, where the social ben-efits available in general (and to mothers in particular) are quite generous. This is incontrast to the results from e.g. Abrevaya and Dahl (2008). They find, for instance,that marital status is highly significant. A reason for this difference could be thatAmerica has a substantial social gap compared to Denmark. This will undoubtedlyhave consequences for unmarried mothers in America, who do not have the samesocial benefits as offered in Denmark. Another, perhaps more subtle reason could bethe extent to which marriage can proxy for unobserved characteristics or ability ofwomen. The choice of why and when to get married may be culturally dependent,which is supported by the descriptive statistics. There is quite a difference in propor-tions of pregnancies in and out of wedlock in their American data and our Danishdata, which suggests that it is more uncommon to have children out of wedlock inAmerica. When combined, these arguments may be used to explain why the Ameri-can data suggest that marriage has a positive effect and no such evidence is found inthe Danish data.

Abrevaya and Dahl also find that education has a significant effect, while we findlittle evidence of such an effect. This could very well be due to the costs associatedwith education in America. This is in contrast to Denmark where education is free.The variable may therefore proxy for wealth status which, as argued before, seemsirrelevant in Denmark.

The mother’s characteristics are largely insignificant in the “main” terms of theCREM specification (those in Xmb). The augmented CRE terms, however, do showsome significance (those in Sm). This could be interpreted as a “part” of the hetero-


geneity, e.g. for weight: the overall stature of the mother can be more important thanbirth-specific fluctuations. Height, is highly significant. However, no extra CRE vari-able is constructed for height because it is birth-invariant. The fact that the height andweight variables are significant, for one part of the specification or the other, seemsvery natural. What is puzzling, though, is that age does not appear to have much sig-nificance. Abrevaya and Dahl (2008) find a significant effect of age, and the literaturesuggests that there is an optimal age, see e.g. Royer (2004).

For these variables the fixed effects models differ considerably. First, becauseheight is birth invariant it cannot be included in these models and should instead becaptured by the fixed effect. Second, weight is in most cases significant. This is tobe expected as it cannot be captured by the fixed effects, but will most likely affectbirthweight. Finally, age does show moderate signs of significance in some of thefixed effects specifications, but not to a degree where we are confident enough todraw any firm conclusions.

Regarding child characteristics, we find that the parity variables second, third andfourth child, and male child are significant and positive across all quantiles. This is tobe expected since it is generally acknowledged that the birthweight of male childrenis higher on average, and that birthweight increases with parity of the mother. Thisconfirms the results of previous studies.

5 Concluding remarks

In this paper we have found strong evidence that smoking during pregnancy has ad-verse consequences for birthweight outcomes. The documented connection betweenbabies’ birthweight and their overall health, along with the costs associated with lowbirthweight, makes this a very important result. The effect appears to worsen the fur-ther one moves to the left in the birthweight distribution, especially when measuredrelative to birthweight at the corresponding quantiles.

The significant effect of smoking has been documented before, but we add tothese results in several ways. The richness of the applied data set allowed us to controlfor many potentially important characteristics which were not included in previousstudies. Furthermore, we use several estimators and provide a detailed discussionof their differences in interpretation and performance. Given the results from thisbattery of estimators, the adverse effect of smoking on birthweight seems irrefutable,regardless of estimation approach and which of the two discussed interpretations isdesired for the estimated coefficients.

As icing on the cake, our analysis used information on smoking behavior priorto pregnancy, allowing for a separation of effects. Only smoking during pregnancyhas a pronounced significant effect, a result speaking for intervention campaigns as aworthwhile activity.


Acknowledgements We are grateful Jason Abrevaya, Niels Haldrup, Marianne Simonsen, Chiara Orsini,Ulrich Kaiser, Tine B. Henriksen, and Kirsten Wisborg for helpful comments. Lise V. Hansen offeredinvaluable assistance by providing access to the data from Aarhus University Hospital, Skejby. The termsof the data-sharing agreements do not allow release of these data. However, codes for estimation in R areavailable from the corresponding author upon request. We would also also like to thank Roger Koenker foruseful discussion and for writing the quantreg package for R that was used as starting point for the quantileestimations in this paper. The authors gratefully acknowledge financial support from the Danish SocialSciences Research Council (grant 275-06-0105) and the Center for Research in Econometric Analysis ofTime Series, CREATES, funded by The Danish National Research Foundation.


A Simulation results

B = 2 B = 3 B = 5τ M = 499 M = 999 M = 499 M = 999 M = 499 M = 999

Cro

ss-s

ectio

nF

Eta

rget

0.25 −0.3380 −0.3402 −0.3412 −0.3443 −0.3435 −0.3405(0.3713) (0.3561) (0.3618) (0.3538) (0.3560) (0.3467)

0.50 −0.3724 −0.3740 −0.3755 −0.3718 −0.3718 −0.3722(0.3968) (0.3867) (0.3920) (0.3808) (0.3813) (0.3770)

0.75 −0.4321 −0.4344 −0.4310 −0.4282 −0.4186 −0.4245(0.4598) (0.4468) (0.4489) (0.4373) (0.4301) (0.4303)

Dum

my

regr

essi

on

0.25 0.6717 0.6626 0.3531 0.3474 0.1438 0.1431(0.6980) (0.6770) (0.3813) (0.3619) (0.1763) (0.1595)

0.50 −0.0028 −0.0119 −0.0047 −0.0055 −0.0035 −0.0053(0.1898) (0.1395) (0.1272) (0.0904) (0.0865) (0.0645)

0.75 −0.6773 −0.6864 −0.3596 −0.3598 −0.1438 −0.1475(0.7033) (0.7003) (0.3877) (0.3736) (0.1752) (0.1645)

KFE

3

0.25 −0.0873 −0.0958 −0.0493 −0.0513 −0.0927 −0.0911(0.1872) (0.1486) (0.1283) (0.0981) (0.1322) (0.1129)

0.50 −0.1391 −0.1425 −0.1534 −0.1530 −0.1426 −0.1444(0.2089) (0.1818) (0.1887) (0.1722) (0.1641) (0.1560)

0.75 −0.3664 −0.3694 −0.2452 −0.2396 −0.1828 −0.1889(0.3977) (0.3852) (0.2753) (0.2547) (0.2062) (0.2009)

KFE

3Po

stes

t.

0.25 0.0877 0.0807 0.1105 0.1081 0.0614 0.0600(0.1967) (0.1425) (0.1682) (0.1421) (0.1157) (0.0905)

0.50 −0.0224 −0.0321 −0.0474 −0.0430 −0.0253 −0.0269(0.1821) (0.1357) (0.1264) (0.0951) (0.0875) (0.0676)

0.75 −0.2531 −0.2582 −0.2052 −0.2002 −0.1040 −0.1086(0.3030) (0.2844) (0.2476) (0.2207) (0.1431) (0.1279)

KFE

1

0.25 −0.1993 −0.2071 −0.1275 −0.1322 −0.1027 −0.1006(0.2582) (0.2368) (0.1725) (0.1542) (0.1395) (0.1207)

0.50 −0.2239 −0.2315 −0.1827 −0.1818 −0.1331 −0.1344(0.2615) (0.2520) (0.2144) (0.1989) (0.1570) (0.1477)

0.75 −0.3690 −0.3749 −0.2996 −0.2943 −0.2865 −0.2934(0.3980) (0.3902) (0.3247) (0.3066) (0.3009) (0.3008)

2SFE

0.25 0.3921 0.3844 0.2598 0.2551 0.1563 0.1553(0.4285) (0.4014) (0.2882) (0.2707) (0.1844) (0.1687)

0.50 −0.0020 −0.0110 −0.0208 −0.0210 −0.0259 −0.0267(0.1640) (0.1169) (0.1162) (0.0844) (0.0879) (0.0664)

0.75 −0.4036 −0.4080 −0.3004 −0.2981 −0.1961 −0.2005(0.4355) (0.4249) (0.3262) (0.3101) (0.2155) (0.2104)

Cro

ss-s

ectio

nC

RE

targ

et

0.25 −0.3825 −0.3848 −0.3858 −0.3889 −0.3881 −0.3851(0.4123) (0.3989) (0.4042) (0.3973) (0.3992) (0.3906)

0.50 −0.3724 −0.3740 −0.3755 −0.3718 −0.3718 −0.3722(0.3968) (0.3867) (0.3920) (0.3808) (0.3813) (0.3770)

0.75 −0.3875 −0.3898 −0.3864 −0.3836 −0.3740 −0.3799(0.4182) (0.4036) (0.4063) (0.3937) (0.3869) (0.3864)

CR

EM

0.25 −0.0164 −0.0253 −0.0225 −0.0247 −0.0210 −0.0185(0.2063) (0.1416) (0.1439) (0.1029) (0.1020) (0.0739)

0.50 −0.0004 −0.0092 −0.0103 −0.0073 −0.0062 −0.0071(0.1749) (0.1237) (0.1290) (0.0916) (0.0904) (0.0638)

0.75 −0.0018 −0.0052 0.0048 0.0057 0.0144 0.0093(0.2017) (0.1398) (0.1431) (0.1030) (0.1045) (0.0745)

AD

0.25 −0.0126 −0.0247 −0.0217 −0.0227 −0.0191 −0.0181(0.2028) (0.1399) (0.1432) (0.1029) (0.1021) (0.0728)

0.50 0.0005 −0.0093 −0.0086 −0.0077 −0.0066 −0.0071(0.1723) (0.1237) (0.1287) (0.0919) (0.0905) (0.0635)

0.75 −0.0066 −0.0060 0.0028 0.0062 0.0127 0.0095(0.2018) (0.1391) (0.1424) (0.1026) (0.1046) (0.0749)

Table 8: Bias and root mean squared error (rmse) for simulation of (23) with γ = 0,i.e. no scale effect of the individual effects.


B = 2 B = 3 B = 5τ M = 499 M = 999 M = 499 M = 999 M = 499 M = 999

Cro

ss-s

ectio

nF

Eta

rget

0.25 −0.1453 −0.1508 −0.1465 −0.1493 −0.1482 −0.1487(0.1853) (0.1688) (0.1739) (0.1641) (0.1671) (0.1591)

0.50 −0.4118 −0.4218 −0.4112 −0.4131 −0.4159 −0.4170(0.4326) (0.4307) (0.4252) (0.4205) (0.4240) (0.4213)

0.75 −0.5625 −0.5662 −0.5608 −0.5582 −0.5664 −0.5645(0.5855) (0.5777) (0.5774) (0.5665) (0.5753) (0.5698)

Dum

my

regr

essi

on

0.25 0.6746 0.6619 0.4037 0.4078 0.2317 0.2344(0.6973) (0.6714) (0.4241) (0.4179) (0.2482) (0.2430)

0.50 −0.0000 −0.0127 −0.0027 0.0003 −0.0020 −0.0005(0.1766) (0.1134) (0.1126) (0.0826) (0.0761) (0.0573)

0.75 −0.6744 −0.6871 −0.4076 −0.4071 −0.2327 −0.2313(0.6971) (0.6963) (0.4270) (0.4179) (0.2478) (0.2395)

KFE

3

0.25 0.1404 0.1339 0.2401 0.2387 0.1974 0.2002(0.1979) (0.1605) (0.2655) (0.2514) (0.2160) (0.2099)

0.50 −0.1861 −0.1970 −0.1769 −0.1756 −0.1575 −0.1571(0.2367) (0.2179) (0.2049) (0.1910) (0.1745) (0.1667)

0.75 −0.5255 −0.5303 −0.4710 −0.4708 −0.4405 −0.4393(0.5514) (0.5426) (0.4889) (0.4803) (0.4517) (0.4452)

KFE

3Po

stes

t.

0.25 0.3908 0.3829 0.3568 0.3556 0.3281 0.3289(0.4276) (0.3999) (0.3795) (0.3667) (0.3424) (0.3363)

0.50 −0.0235 −0.0364 −0.0378 −0.0369 −0.0209 −0.0185(0.1717) (0.1140) (0.1137) (0.0866) (0.0778) (0.0593)

0.75 −0.5240 −0.5309 −0.4238 −0.4220 −0.3684 −0.3682(0.5515) (0.5447) (0.4442) (0.4331) (0.3797) (0.3745)

KFE

1

0.25 −0.0206 −0.0255 0.0462 0.0446 0.0653 0.0668(0.1284) (0.0848) (0.1107) (0.0834) (0.1002) (0.0874)

0.50 −0.2401 −0.2503 −0.1690 −0.1690 −0.1137 −0.1118(0.2737) (0.2633) (0.1992) (0.1855) (0.1363) (0.1257)

0.75 −0.5009 −0.5108 −0.4130 −0.4143 −0.4239 −0.4217(0.5255) (0.5229) (0.4299) (0.4235) (0.4341) (0.4272)

2SFE

0.25 0.5075 0.5054 0.3986 0.3962 0.2813 0.2839(0.5331) (0.5167) (0.4157) (0.4048) (0.2940) (0.2902)

0.50 −0.0004 −0.0091 −0.0226 −0.0220 −0.0273 −0.0270(0.1585) (0.1052) (0.1112) (0.0823) (0.0799) (0.0611)

0.75 −0.5913 −0.5983 −0.5150 −0.5165 −0.4201 −0.4197(0.6162) (0.6104) (0.5314) (0.5256) (0.4294) (0.4250)

Cro

ss-s

ectio

nC

RE

targ

et

0.25 −0.2084 −0.2139 −0.2095 −0.2124 −0.2113 −0.2118(0.2380) (0.2269) (0.2296) (0.2230) (0.2249) (0.2192)

0.50 −0.3865 −0.3965 −0.3859 −0.3878 −0.3906 −0.3918(0.4087) (0.4060) (0.4008) (0.3957) (0.3992) (0.3963)

0.75 −0.5083 −0.5120 −0.5066 −0.5040 −0.5122 −0.5104(0.5336) (0.5247) (0.5250) (0.5132) (0.5220) (0.5162)

CR

EM

0.25 −0.0061 −0.0116 −0.0107 −0.0126 −0.0256 −0.0243(0.1600) (0.1084) (0.1138) (0.0802) (0.0853) (0.0649)

0.50 −0.0217 −0.0310 −0.0118 −0.0095 −0.0066 −0.0081(0.1890) (0.1255) (0.1254) (0.0945) (0.0911) (0.0657)

0.75 −0.0002 −0.0084 −0.0031 −0.0048 −0.0144 −0.0103(0.2146) (0.1518) (0.1538) (0.1107) (0.1075) (0.0784)

AD

0.25 −0.0076 −0.0137 −0.0129 −0.0132 −0.0232 −0.0231(0.1586) (0.1056) (0.1161) (0.0803) (0.0842) (0.0646)

0.50 −0.0201 −0.0271 −0.0115 −0.0094 −0.0059 −0.0089(0.1889) (0.1243) (0.1274) (0.0939) (0.0901) (0.0659)

0.75 0.0010 −0.0063 −0.0017 −0.0053 −0.0149 −0.0103(0.2167) (0.1513) (0.1491) (0.1102) (0.1072) (0.0792)

Table 9: Bias and root mean squared error (rmse) for simulation of (23) with γ = 1,i.e. the individual effects have scale effects.


B Empirical results


10% 25% 50% 75% 90% OLS

Smoked during -231.362 *** -174.003 *** -57.873 -126.478 *** 12.694 -109.920 ***

(58.602) (39.997) (35.973) (44.777) (61.797) (27.174)

Smoked before -14.954 -9.730 -14.592 -21.266 -32.916 -17.915(45.387) (32.215) (26.704) (32.912) (47.865) (21.165)

Drink 2.451 -14.800 -34.876 -70.408 * -59.946 -56.370 *

(62.183) (46.010) (37.541) (40.433) (54.935) (30.156)

Birth control pills -34.450 -53.682 *** -30.988 * -19.569 -22.692 -33.379 ***

(27.588) (18.999) (17.313) (19.016) (27.585) (12.648)

Complications -100.794 *** -61.137 *** -26.939 * -23.624 2.355 -54.648 ***

(30.312) (20.413) (14.485) (17.466) (24.221) (13.054)

Doctor visits 6.119 18.112 * 16.192 ** 11.760 8.599 15.857 *

(12.870) (9.804) (8.155) (8.255) (11.528) (8.399)

Prenatal visits 92.698 *** 84.246 *** 74.827 *** 74.228 *** 79.509 *** 55.543 ***

(15.312) (8.311) (5.941) (5.990) (7.938) (13.689)

Test tube baby 20.611 -27.565 -0.812 -40.657 -181.511 * -54.088(127.855) (79.473) (65.856) (73.092) (97.172) (50.084)

Diabetes 103.043 150.006 * 256.696 *** 285.550 *** 282.415 *** 221.760 ***

(121.416) (84.986) (70.130) (63.294) (95.084) (68.298)

Income -0.080 -0.016 -0.122 -0.048 -0.100 -0.114(0.365) (0.270) (0.221) (0.255) (0.347) (0.178)

Unemployment benefits -0.430 -0.112 0.034 -0.220 -0.190 -0.328(0.612) (0.457) (0.373) (0.428) (0.596) (0.298)

Home size -0.255 -0.316 0.138 0.115 0.039 -0.114(0.275) (0.219) (0.204) (0.255) (0.306) (0.154)

Married -2.424 -2.771 -3.197 13.586 -29.501 9.930(32.435) (24.068) (18.997) (22.819) (30.852) (15.214)

Student 1.707 5.730 9.500 27.206 38.908 11.019(38.078) (25.659) (21.703) (25.454) (35.496) (16.583)

Height 6.879 *** 9.110 *** 10.965 *** 11.956 *** 11.858 *** 10.711 ***

(1.676) (1.242) (1.095) (1.185) (1.496) (1.009)

Weight 14.741 6.959 8.628 11.938 18.380 14.603 *

(19.519) (13.179) (11.240) (11.493) (14.762) (8.772)

Weight2 -0.088 -0.016 -0.051 -0.080 -0.092 -0.085(0.134) (0.091) (0.077) (0.078) (0.099) (0.060)

Age -20.490 -14.207 -44.707 ** -55.060 ** -59.251 -51.252 ***

(44.525) (29.026) (21.477) (24.239) (36.313) (18.965)

Age2 0.446 0.272 0.801 ** 0.940 ** 1.034 * 0.943 ***

(0.689) (0.463) (0.348) (0.390) (0.588) (0.303)

Second child 172.737 *** 176.777 *** 161.944 *** 167.637 *** 173.776 *** 161.824 ***

(38.773) (25.237) (20.194) (22.451) (32.241) (18.413)

Male child 122.307 *** 143.390 *** 142.821 *** 174.666 *** 204.769 *** 152.488 ***

(19.951) (14.244) (12.124) (13.834) (18.670) (9.888)

Education Cat. 1 89.874 -88.905 -50.289 14.492 47.121 -42.019(117.650) (82.602) (59.506) (65.153) (79.828) (57.275)

Education Cat. 2 127.210 -45.128 10.293 77.617 140.297 * 30.576(112.123) (80.818) (58.588) (63.556) (78.042) (56.087)

Education Cat. 3 143.775 -16.251 -9.094 68.587 129.169 30.857(119.275) (82.667) (62.246) (68.082) (84.486) (59.790)

Education Cat. 4 142.865 -34.228 19.312 110.734 * 141.894 * 43.511(113.361) (80.779) (59.365) (65.097) (80.660) (58.183)

Education Cat. 5 179.570 -1.531 14.288 91.657 168.319 * 54.905(119.177) (81.216) (61.821) (67.131) (86.391) (60.299)

Education Cat. 6 168.811 -1.022 30.895 91.665 156.424 * 61.238(115.427) (83.092) (60.580) (65.951) (83.129) (58.816)

Education Cat. 7 214.014 23.381 38.629 154.758 123.545 68.702(160.280) (120.056) (95.431) (104.422) (110.882) (89.514)

Asterisks denote the significance level (double-sided). *: 10%, **: 5%, ***: 1%.Bootstrapped standard errors are given in parentheses. The bootstrap was done using a sample size of 3,000 births and 499iterations.

Table 10: Estimation results from the AD model using the balanced dataset. Mainvariables.



10% 25% 50% 75% 90% OLS

Smoked during (i) 34.427 17.522 -52.118 * 19.774 -32.024 -17.594(48.437) (33.175) (30.156) (36.824) (51.533) (26.501)

Smoked during (ii) 37.590 -21.545 -77.352 ** -88.525 ** -184.486 *** -71.036 **

(48.435) (37.411) (34.246) (41.459) (54.086) (31.282)

Smoked before (i) 21.684 28.449 12.392 -6.865 18.485 18.441(33.333) (26.032) (22.050) (26.626) (38.512) (18.975)

Smoked before (ii) -4.789 16.983 12.363 52.183 * 54.067 23.716(39.965) (30.875) (27.373) (30.820) (42.059) (23.153)

Drink (i) 8.472 -15.287 -9.150 17.372 -7.084 14.925(45.042) (43.505) (37.213) (42.717) (52.395) (30.150)

Drink (ii) -43.062 17.824 54.152 12.678 -6.692 34.730(55.961) (45.819) (35.595) (39.593) (59.906) (35.509)

Birth control pills (i) -7.967 12.434 -12.738 -17.245 -26.740 -13.656(25.764) (18.860) (16.818) (18.882) (25.430) (13.801)

Birth control pills (ii) 34.883 50.037 ** 18.906 20.941 32.899 37.296 **

(27.015) (20.325) (17.742) (18.587) (28.468) (15.719)

Complications (i) -65.146 ** -26.441 -22.255 -17.894 -11.197 -37.698 **

(26.855) (18.963) (14.585) (18.625) (24.055) (15.105)

Complications (ii) -88.984 *** -55.124 *** -31.961 ** -31.331 * -42.418 * -57.531 ***

(27.224) (20.279) (15.756) (16.976) (24.115) (14.989)

Doctor visits (i) 4.390 -2.316 1.404 -1.955 6.506 9.751(12.360) (9.992) (8.851) (9.915) (13.147) (8.532)

Doctor visits (ii) 1.283 -3.983 -1.185 -4.714 -8.715 -3.847(12.543) (9.229) (8.435) (8.106) (11.210) (7.503)

Prenatal visits (i) 29.114 ** 30.386 *** 36.961 *** 38.947 *** 30.897 *** 27.070 **

(12.883) (9.344) (6.827) (6.081) (7.713) (11.495)

Prenatal visits (ii) 0.370 -0.392 2.953 3.607 -0.300 0.848(9.028) (5.291) (4.562) (5.091) (5.969) (6.655)

Test tube baby (i) 46.405 32.526 44.364 17.930 91.791 62.780(108.364) (65.722) (53.476) (72.293) (110.727) (55.740)

Test tube baby (ii) -41.714 20.727 -30.053 78.943 147.260 * 38.015(101.538) (82.967) (77.418) (84.050) (82.467) (62.333)

Income (i) 0.211 0.154 -0.276 -0.390 -0.390 -0.143(0.328) (0.268) (0.243) (0.282) (0.365) (0.213)

Income (ii) 0.110 0.005 0.082 0.047 -0.001 0.083(0.326) (0.245) (0.194) (0.198) (0.266) (0.167)

Unemployment benefits (i) -0.305 -0.689 -0.689 * -0.578 -0.780 -0.540(0.555) (0.430) (0.388) (0.449) (0.541) (0.337)

Unemployment benefits (ii) 0.342 0.439 0.542 0.847 ** 0.719 0.727 **

(0.571) (0.479) (0.380) (0.388) (0.565) (0.328)

Home size (i) 0.268 0.376 * -0.071 0.208 0.183 0.192(0.225) (0.207) (0.192) (0.228) (0.252) (0.163)

Home size (ii) 0.197 0.322 0.086 0.140 0.059 0.220(0.269) (0.207) (0.171) (0.192) (0.271) (0.143)

Married (i) -35.504 -21.928 -2.066 -6.983 17.387 -22.931(23.669) (19.285) (16.372) (19.568) (25.276) (15.421)

Married (ii) 10.370 -0.958 -12.085 -20.238 10.430 -3.058(26.864) (21.047) (16.674) (19.218) (27.180) (14.911)

Student (i) 48.297 38.346 * 23.560 4.320 -2.628 23.562(30.253) (22.501) (20.822) (25.053) (35.786) (18.565)

Student (ii) 21.763 16.683 -7.744 -12.135 -3.007 6.474(34.996) (26.086) (22.569) (23.948) (31.045) (19.320)

Weight (i) -2.419 -6.812 -7.124 -22.844 ** -25.814 * -11.814(16.352) (10.952) (9.852) (11.132) (13.401) (8.255)

Weight (ii) 11.216 22.988 ** 21.388 ** 26.031 *** 23.605 ** 18.239 **

(14.437) (10.603) (9.404) (9.048) (11.045) (7.457)

Weight2 (i) -0.010 0.004 0.018 0.140 * 0.153 * 0.050(0.112) (0.075) (0.069) (0.078) (0.092) (0.057)

Weight2 (ii) -0.029 -0.109 -0.079 -0.113 * -0.110 -0.063(0.100) (0.073) (0.065) (0.062) (0.072) (0.052)

Age (i) 34.032 -0.010 -17.079 -19.052 -20.056 -0.984(57.090) (43.502) (32.998) (38.446) (50.820) (31.604)

Age (ii) 26.236 30.125 77.768 ** 58.312 80.949 65.563 *

(63.144) (44.987) (34.394) (38.459) (55.363) (33.800)

Age2 (i) -0.679 -0.107 0.193 0.326 0.362 -0.051(0.998) (0.764) (0.593) (0.679) (0.920) (0.560)

Age2 (ii) -0.514 -0.461 -1.216 ** -0.947 -1.311 -1.091 **

(1.038) (0.725) (0.561) (0.636) (0.927) (0.551)

Male child (i) -18.425 -32.615 ** -25.624 * -33.839 ** -13.955 -30.625 ***

(19.717) (14.770) (13.300) (14.540) (19.145) (11.199)

Male child (ii) 11.833 -5.623 -9.206 -14.778 -51.292 *** -5.882(19.609) (15.003) (12.137) (14.254) (18.668) (11.647)


Table 11: Estimation results from the AD model using the balanced dataset. CREadded variables.



10% 25% 50% 75% 90% OLS

Smoked during -190.485 *** -112.107 *** -75.991 *** -90.337 *** -2.081 -94.897 ***

(49.047) (35.800) (27.952) (34.573) (49.101) (23.618)

Smoked before -6.101 -14.429 -30.103 -36.834 -47.618 -21.863(35.629) (27.941) (24.240) (26.244) (37.643) (19.926)

Drink 11.578 -47.183 -33.420 -45.828 -13.504 -42.091(51.397) (37.665) (34.045) (36.649) (49.262) (26.156)

Birth control pills -27.853 -52.478 *** -28.928 ** -21.657 -19.116 -33.813 ***

(25.097) (18.130) (14.118) (16.678) (22.708) (11.650)

Complications -122.386 *** -67.361 *** -46.073 *** -29.562 ** -11.029 -65.723 ***

(24.632) (16.595) (12.271) (14.727) (21.520) (10.636)

Doctor visits 5.378 10.838 15.874 ** 11.317 -0.099 12.845 *

(10.409) (8.081) (6.916) (7.094) (10.166) (6.765)

Prenatal visits 109.582 *** 90.162 *** 77.477 *** 80.245 *** 73.484 *** 64.011 ***

(11.583) (5.906) (4.583) (5.080) (6.969) (11.670)

Test tube baby -2.683 64.214 30.674 -57.277 -251.771 *** -34.417(108.153) (70.387) (61.737) (63.434) (86.622) (46.240)

Diabetes 181.554 * 217.704 *** 280.896 *** 315.398 *** 373.631 *** 282.529 ***

(94.004) (70.214) (55.456) (62.333) (88.341) (54.962)

Income -0.126 -0.126 -0.088 -0.127 -0.120 -0.108(0.276) (0.196) (0.183) (0.203) (0.284) (0.135)

Unemployment benefits -0.303 -0.185 -0.135 -0.468 0.128 -0.410 *

(0.510) (0.358) (0.311) (0.350) (0.484) (0.239)

Home size -0.219 0.016 -0.010 0.042 -0.079 -0.072(0.268) (0.191) (0.180) (0.225) (0.294) (0.143)

Married -5.950 -1.556 -2.479 -6.801 -19.225 -4.313(27.684) (19.025) (16.058) (19.336) (27.507) (13.429)

Student 20.743 4.311 1.137 10.260 51.933 * 17.787(31.961) (22.674) (21.060) (22.319) (29.430) (15.434)

Height 6.662 *** 8.423 *** 10.489 *** 11.419 *** 11.183 *** 10.269 ***

(1.525) (1.088) (0.975) (1.074) (1.320) (0.906)

Weight 5.722 2.412 -8.622 2.040 23.161 ** 7.950(14.546) (9.823) (8.403) (8.182) (11.050) (6.514)

Weight2 -0.026 0.008 0.063 -0.010 -0.127 * -0.036(0.099) (0.066) (0.058) (0.054) (0.071) (0.043)

Age -40.769 -24.258 -19.409 -29.653 * -0.204 -14.971(30.152) (20.280) (16.161) (17.768) (26.393) (14.840)

Age2 0.867 * 0.516 0.402 0.465 0.065 0.333(0.467) (0.319) (0.256) (0.285) (0.420) (0.236)

Second child 177.725 *** 162.143 *** 150.112 *** 175.701 *** 156.739 *** 162.162 ***

(21.562) (14.632) (12.540) (14.267) (19.457) (11.515)

Third child 213.334 *** 191.121 *** 190.076 *** 252.706 *** 231.066 *** 209.153 ***

(33.522) (24.012) (22.312) (24.301) (31.575) (20.485)

Fourth child 172.238 *** 182.380 *** 181.915 *** 233.246 *** 202.214 *** 191.631 ***

(56.800) (41.156) (37.683) (40.316) (51.240) (34.217)

Male child 121.921 *** 128.415 *** 137.299 *** 162.926 *** 186.615 *** 145.904 ***

(16.220) (12.039) (10.115) (12.611) (16.705) (8.042)

Education Cat. 1 -17.762 -76.618 -81.724 -39.997 -9.637 -62.830(90.017) (63.440) (54.685) (51.733) (62.760) (44.738)

Education Cat. 2 40.745 -39.634 -34.390 17.789 63.845 -5.916(86.174) (60.040) (51.815) (50.007) (59.730) (44.813)

Education Cat. 3 84.970 -8.360 -37.973 -6.862 31.144 -7.380(92.000) (63.567) (56.402) (55.421) (64.993) (46.993)

Education Cat. 4 57.207 -29.640 -18.659 30.217 85.484 9.992(85.169) (59.404) (52.030) (50.103) (61.687) (44.595)

Education Cat. 5 67.216 -30.498 -59.437 9.144 77.633 -2.762(93.874) (65.271) (55.834) (59.343) (69.266) (49.610)

Education Cat. 6 80.965 1.085 -12.183 19.262 66.071 22.282(86.395) (62.012) (55.002) (53.307) (67.144) (46.642)

Education Cat. 7 56.158 -22.984 -48.886 3.971 40.766 -18.372(157.415) (96.129) (87.963) (96.698) (147.423) (82.569)


Table 12: Estimation results from the CREM model using the unbalanced dataset.Main variables.



10% 25% 50% 75% 90% OLS

Smoked during 1.511 -81.205 * -118.446 *** -118.538 *** -224.515 *** -123.482 ***

(60.811) (47.264) (36.936) (44.050) (57.950) (30.579)

Smoked before -2.960 36.036 31.171 63.577 * 88.842 * 45.941 *

(43.834) (34.982) (30.794) (33.820) (47.633) (26.418)

Drink -41.244 12.411 37.354 -0.066 -56.913 18.728(67.546) (58.164) (45.985) (52.983) (70.383) (37.602)

Birth control pills 20.963 42.465 3.423 -5.526 -5.043 13.155(34.027) (26.099) (22.278) (25.759) (34.068) (18.917)

Complications -135.696 *** -75.278 *** -38.337 * -44.836 * -34.767 -79.684 ***

(35.896) (24.149) (20.843) (24.062) (31.528) (17.880)

Doctor visits 10.269 1.704 -3.187 -1.286 0.357 5.962(16.818) (11.226) (10.423) (12.417) (17.171) (8.744)

Prenatal visits 8.670 18.729 ** 31.123 *** 28.191 *** 19.459 ** 20.307 ***

(8.377) (8.150) (7.073) (7.784) (9.857) (6.213)

Test tube baby 9.859 -63.569 -5.916 101.877 312.990 ** 53.572(136.485) (97.028) (80.492) (97.485) (129.928) (69.107)

Income 0.327 0.248 0.106 0.100 0.018 0.134(0.315) (0.252) (0.225) (0.255) (0.354) (0.175)

Unemployment benefits 0.503 0.260 0.591 0.938 * 0.165 0.791 *

(0.711) (0.542) (0.498) (0.556) (0.743) (0.404)

Home size 0.504 0.262 0.253 0.223 0.272 0.322 *

(0.317) (0.250) (0.220) (0.276) (0.342) (0.193)

Married 2.626 -11.628 -5.422 13.333 36.962 1.738(32.593) (22.949) (19.948) (22.826) (31.406) (16.984)

Student 42.309 50.671 58.122 ** 36.587 -10.418 35.052(40.198) (31.235) (27.134) (29.995) (40.104) (22.354)

Weight 18.993 25.524 ** 33.761 *** 18.262 ** -0.876 16.575 **

(14.521) (10.053) (9.554) (8.925) (12.387) (7.507)

Weight2 -0.106 -0.158 ** -0.188 *** -0.078 0.035 -0.084 *

(0.098) (0.067) (0.067) (0.060) (0.080) (0.050)

Age 52.479 33.363 20.231 7.749 5.752 16.427(39.830) (27.214) (21.470) (24.502) (34.454) (20.514)

Age2 -1.115 * -0.702 -0.460 -0.112 -0.163 -0.382(0.644) (0.438) (0.352) (0.398) (0.550) (0.332)

Male child -15.270 -30.872 -34.649 * -41.648 ** -46.620 * -30.403 **

(25.973) (20.708) (18.213) (19.345) (24.349) (15.446)


Table 13: Estimation results from the CREM model using the unbalanced dataset. CREadded variables.



10% 25% 50% 75% 90% OLS

Smoked during -70.869 *** -83.486 *** -99.452 *** -104.189 *** -108.669 *** -94.360 ***

(26.305) (21.007) (19.840) (20.379) (24.320) (19.320)

Smoked before -55.565 *** -41.376 *** -19.328 -10.835 -3.529 -24.233 *

(18.267) (15.541) (14.587) (15.951) (18.783) (14.206)

Drink -24.374 -22.919 -44.797 * -51.251 ** -59.697 * -39.255 *

(29.747) (24.710) (25.253) (25.508) (30.727) (23.552)

Birth control pills -36.884 ** -31.089 ** -37.452 *** -30.736 ** -27.382 * -34.084 ***

(14.850) (12.219) (11.802) (12.597) (14.772) (11.521)

Complications -96.524 *** -74.428 *** -54.155 *** -31.219 *** -22.950 * -64.428 ***

(16.128) (12.741) (11.166) (11.377) (13.732) (11.104)

Doctor visits 14.708 * 10.948 12.629 * 13.281 ** 9.717 12.974 *

(8.338) (7.224) (6.623) (6.666) (6.830) (7.323)

Prenatal visits 76.715 *** 70.372 *** 69.121 *** 69.656 *** 68.376 *** 62.657 ***

(14.315) (10.600) (9.265) (8.646) (8.266) (13.404)

Test tube baby -45.804 -53.412 -18.727 -50.580 -39.651 -35.884(56.989) (47.253) (39.209) (40.931) (48.205) (40.673)

Income -0.094 -0.095 -0.114 -0.136 -0.135 -0.109(0.147) (0.124) (0.119) (0.127) (0.152) (0.116)

Unemployment benefits -0.311 -0.259 -0.411 -0.231 -0.247 -0.365(0.347) (0.275) (0.258) (0.270) (0.326) (0.255)

Home size -0.043 -0.128 -0.098 -0.007 -0.120 -0.086(0.145) (0.120) (0.115) (0.122) (0.138) (0.112)

Married -1.042 -1.205 -1.521 -4.776 -4.244 -1.310(13.302) (11.668) (10.787) (11.433) (13.451) (10.709)

Student 37.874 ** 14.307 5.707 3.321 -16.208 5.924(17.172) (14.461) (13.833) (14.664) (17.734) (13.347)

Weight 6.290 9.372 ** 7.402 ** 5.478 10.136 ** 7.808 **

(4.425) (3.942) (3.468) (3.594) (4.093) (3.539)

Weight2 -0.036 -0.052 * -0.033 -0.015 -0.042 -0.036(0.031) (0.027) (0.024) (0.025) (0.028) (0.024)

Age -9.353 -20.214 -24.367 ** -28.692 ** -40.657 *** -23.597 *

(16.801) (13.553) (12.277) (12.582) (14.517) (12.242)

Age2 0.009 0.177 0.254 0.350 * 0.541 ** 0.245(0.278) (0.228) (0.206) (0.210) (0.241) (0.204)

Second child 153.467 *** 156.642 *** 159.453 *** 148.996 *** 150.982 *** 154.368 ***

(13.608) (11.138) (10.753) (10.909) (13.908) (10.496)

Third child 173.195 *** 184.148 *** 196.344 *** 194.057 *** 201.286 *** 187.332 ***

(23.305) (19.337) (18.227) (19.007) (23.195) (18.328)

Fourth child 183.072 *** 207.923 *** 206.771 *** 203.407 *** 208.761 *** 194.235 ***

(45.266) (39.430) (35.272) (36.674) (44.848) (35.431)

Male child 144.927 *** 140.211 *** 142.491 *** 149.684 *** 143.478 *** 145.187 ***

(11.433) (9.381) (8.734) (9.158) (11.089) (8.548)

Education Cat. 1 -38.800 -25.320 27.994 50.535 104.376 ** 21.033(57.321) (33.010) (27.240) (35.568) (50.233) (27.652)

Education Cat. 2 -49.741 -29.418 33.218 57.239 * 110.142 ** 22.576(54.799) (32.347) (27.109) (34.744) (48.344) (26.771)

Education Cat. 3 -57.021 -29.995 31.191 44.736 105.960 ** 18.574(58.305) (35.817) (29.071) (37.073) (51.821) (28.921)

Education Cat. 4 -48.247 -21.351 33.079 52.249 112.424 ** 22.250(56.191) (33.309) (27.153) (34.958) (48.894) (26.871)

Education Cat. 5 -56.763 -17.026 37.185 60.919 113.416 ** 25.409(57.618) (34.794) (29.122) (37.192) (53.932) (28.824)

Education Cat. 6 -41.767 -26.221 36.781 50.065 104.212 ** 21.113(57.214) (33.233) (27.344) (35.580) (50.290) (27.318)

Education Cat. 7 -109.022 -46.016 29.793 34.105 112.564 7.597(90.562) (61.026) (48.152) (65.498) (99.115) (48.731)


Table 14: Estimation results from the 2SFE model using the unbalanced dataset.



10% 25% 50% 75% 90%

Smoked during -162.837 *** -156.775 *** -146.782 *** -186.265 *** -183.502 ***

(34.303) (25.604) (23.264) (24.305) (32.937)

Smoked before -24.508 -14.232 -5.846 12.113 29.442(26.155) (20.022) (17.802) (19.141) (27.079)

Drink -41.675 -33.005 -49.502 * -52.400 * -43.625(38.308) (29.008) (28.939) (29.333) (38.988)

Birth control pills -22.839 -22.815 -24.609 * -7.255 -26.680(19.812) (13.959) (13.109) (13.852) (19.669)

Complications -151.500 *** -93.982 *** -62.792 *** -24.545 * -8.647(20.297) (13.777) (12.187) (13.502) (19.534)

Doctor visits 7.704 8.782 14.639 ** 13.681 ** 8.451(9.085) (7.003) (6.103) (6.370) (8.415)

Prenatal visits 101.149 *** 88.274 *** 82.826 *** 82.325 *** 82.236 ***

(12.888) (7.595) (5.724) (5.359) (6.441)

Test tube baby 43.098 21.891 33.384 5.572 -35.821(68.260) (49.740) (38.826) (44.940) (61.586)

Income 0.010 -0.015 -0.043 -0.070 -0.103(0.183) (0.142) (0.136) (0.153) (0.193)

Unemployment benefits -0.268 -0.277 -0.142 0.142 -0.357(0.411) (0.303) (0.259) (0.305) (0.390)

Home size 0.094 0.157 0.274 ** 0.312 ** 0.318 *

(0.163) (0.142) (0.136) (0.137) (0.178)

Married -7.534 2.276 -1.178 -3.597 -13.208(17.240) (13.761) (13.302) (14.068) (18.967)

Student 86.441 *** 63.563 *** 45.732 *** 24.006 33.635(22.890) (16.876) (17.352) (17.373) (25.137)

Weight 31.928 *** 27.255 *** 27.080 *** 23.050 *** 26.062 ***

(5.952) (5.399) (4.906) (4.881) (5.529)

Weight2 -0.170 *** -0.132 *** -0.127 *** -0.094 *** -0.106 ***

(0.042) (0.038) (0.035) (0.034) (0.039)

Age -4.217 -29.836 * -30.644 ** -32.730 ** -44.297 **

(19.625) (15.671) (13.528) (14.332) (19.300)

Age2 0.058 0.485 * 0.526 ** 0.545 ** 0.733 **

(0.325) (0.259) (0.222) (0.235) (0.318)

Second child 186.303 *** 169.990 *** 161.051 *** 160.180 *** 168.794 ***

(18.279) (13.763) (12.066) (14.487) (19.541)

Third child 167.977 *** 202.422 *** 202.170 *** 220.322 *** 230.686 ***

(30.166) (24.527) (22.574) (24.571) (31.334)

Fourth child 191.796 *** 183.375 *** 204.031 *** 228.417 *** 191.609 ***

(55.278) (46.668) (40.472) (42.210) (54.352)

Male child 146.002 *** 140.324 *** 143.942 *** 152.610 *** 152.521 ***

(14.798) (10.770) (9.261) (10.380) (14.746)

Education Cat. 1 -171.625 * -69.412 33.134 46.669 -78.829(90.106) (73.051) (69.667) (69.450) (80.900)

Education Cat. 2 -74.140 27.718 128.365 * 148.536 ** 41.025(87.029) (69.838) (66.251) (67.651) (80.363)

Education Cat. 3 -31.520 49.709 162.331 ** 142.743 * 21.934(94.834) (78.860) (75.283) (76.471) (91.134)

Education Cat. 4 -72.511 47.528 154.641 ** 173.598 ** 63.779(89.993) (71.321) (66.672) (68.443) (83.084)

Education Cat. 5 -80.900 -1.067 115.933 152.616 ** 85.175(97.066) (79.928) (75.752) (76.968) (90.828)

Education Cat. 6 -39.452 71.311 165.983 ** 162.931 ** 36.387(93.207) (73.391) (69.194) (70.773) (87.325)

Education Cat. 7 -111.444 7.248 183.595 * 172.339 46.874(174.631) (128.867) (106.956) (116.731) (182.347)

Asterisks denote the significance level (double-sided). *: 10%, **: 5%, ***: 1%.Bootstrapped standard errors are given in parentheses. The bootstrap was done using a sample size of3,000 births and 499 iterations.

Table 15: Estimation results from the post estimated KFE(5) model with λ = 0.8 andusing the unbalanced dataset.


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